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Grade 5 math worksheets

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Plot and interpret points

Learning goals

  • Reads ordered pairs correctly.
  • Plots points in the correct locations.
  • Interprets coordinate values in context or geometric figures.
  • Uses coordinate differences to reason about horizontal and vertical distances.

Click problems to add them to your worksheet.

Plot and interpret points 1
Each small shape is centered on a grid point. Which geometric shape is centered at \((3, 2)\)?
Figure for problem 533165

Hints

- Read the x-coordinate first. - Then move to the y-coordinate. - Identify the shape centered at that grid location.

Solution

1. Locate x-coordinate \(3\) on the horizontal axis. 2. Move to y-coordinate \(2\). 3. The shape centered at \((3, 2)\) is a triangle.

Answer

The triangle.
Plot and interpret points 2
Each small shape is centered on a grid point. What are the coordinates of the center of the pentagon?
Figure for problem 533169

Hints

- Find the shape with five sides. - Read the horizontal coordinate first and the vertical coordinate second.

Solution

1. Identify the shape with five sides. 2. Its center aligns with x-coordinate \(7\) and y-coordinate \(2\). 3. Therefore, the center is at \((7, 2)\).

Answer

\((7, 2)\)
Plot and interpret points 3
Point \(K\) is shown on the coordinate plane. What are the coordinates of \(K\)?
Figure for problem 550475

Hints

- Read the horizontal position first. - Then read the vertical position. - Write the two values as an ordered pair.

Solution

1. Point \(K\) is \(4\) units to the right of the y-axis and \(3\) units above the x-axis. 2. Therefore, \(K=(4, 3)\).

Answer

\((4, 3)\)
Plot and interpret points 4
Three points are plotted on the coordinate plane. Which labeled point is at \((2, 6)\)?
Figure for problem 550476

Hints

- Locate x-coordinate \(2\) on the horizontal axis. - Then look at height \(6\). - Match that location to a label.

Solution

1. The point at x-coordinate \(2\) and y-coordinate \(6\) is point \(B\).

Answer

\(B\)
Plot and interpret points 5
Start at point \(P(3, 4)\). Move \(2\) units to the right without moving up or down. What ordered pair gives the new location?

Hints

- Decide which coordinate changes during a horizontal move. - Keep the other coordinate fixed. - Check that the final point is farther right than the starting point.

Solution

1. A rightward move changes only the x-coordinate. 2. The new x-coordinate is \(3+2=5\), and the y-coordinate remains \(4\). 3. The new location is \((5, 4)\).

Answer

\((5, 4)\)
Plot and interpret points 6
On a town map, the first coordinate tells how many blocks east a place is from the starting corner, and the second tells how many blocks north it is. The library is \(2\) blocks east and \(4\) blocks north. Which labeled location is the library? Give the library's ordered pair.
Figure for problem 559056

Hints

- Turn the two distances into one ordered pair before using the graph. - Keep the two numbers in the order used for an ordered pair. - Compare your ordered pair with the labeled points.

Solution

1. The east-west position is the first coordinate, so the first coordinate is \(2\). 2. The north-south position is the second coordinate, so the second coordinate is \(4\). 3. Location R is at \((2, 4)\), so the library should be plotted at R.

Answer

R; \((2, 4)\)
Plot and interpret points 7
A trail map uses a coordinate grid. The first number is the x-coordinate, and the second number is the y-coordinate. The Old Oak is at \(E(2, 3)\), and the Rock Cave is at \(H(7, 1)\). a) A hiker starts at the Old Oak, moves \(4\) units right, and then moves \(2\) units up. At what coordinates does the hiker stop? b) A supply box is buried \(3\) units left of the Rock Cave and \(4\) units above it. Find the coordinates of the box, \(S\).

Hints

- Decide which coordinate changes when you move right or left. - Decide which coordinate changes when you move up or down. - Picture the coordinate grid or make a quick sketch.

Solution

1. Starting at \(E(2, 3)\), moving \(4\) units right changes the x-coordinate to \(2+4=6\). Moving \(2\) units up changes the y-coordinate to \(3+2=5\). The endpoint is \((6, 5)\). 2. Starting at \(H(7, 1)\), moving \(3\) units left changes the x-coordinate to \(7-3=4\). Moving \(4\) units up changes the y-coordinate to \(1+4=5\). Therefore, \(S=(4, 5)\).

Answer

a) \((6, 5)\) b) \(S=(4, 5)\)
Plot and interpret points 8
Four friends’ homes are located on a coordinate grid: - Alex: \(A(2, 8)\) - Bea: \(B(5, 3)\) - Carl: \(C(10, 8)\) - Dana: \(D(5, 8)\) Use the coordinates to answer each question. a) Who lives farthest to the right? b) Which friends live on the same horizontal line? c) Who lives exactly \(5\) units north of Bea?

Hints

- For part a), decide which coordinate controls left-to-right position. - For part b), compare the coordinates of homes that could line up horizontally. - For part c), think about what changes and what stays fixed when you move north on a coordinate grid.

Solution

1. Compare the x-coordinates \(2, 5, 10,\) and \(5\). The greatest is \(10\), so Carl lives farthest to the right. 2. Alex, Carl, and Dana all have y-coordinate \(8\), so their homes lie on the same horizontal line. 3. Moving \(5\) units north from \(B(5, 3)\) gives \((5, 3+5)=(5, 8)\), which is Dana’s location.

Answer

a) Carl b) Alex, Carl, and Dana c) Dana
Plot and interpret points 9
A surveyor records four landmarks on a coordinate map: \(P_1(4.5, 2)\), \(P_2(12, 6.5)\), \(P_3(7, 9)\), and \(P_4(2, 5.5)\). Larger x-values are farther east, and larger y-values are farther north. Find the coordinates of the point that is: a) farthest east. b) farthest north. c) farthest west. d) farthest south.

Hints

- East and west are determined by x-coordinates. - North and south are determined by y-coordinates. - Compare the decimal values carefully.

Solution

1. The greatest x-coordinate is \(12\), so \(P_2(12, 6.5)\) is farthest east. 2. The greatest y-coordinate is \(9\), so \(P_3(7, 9)\) is farthest north. 3. The least x-coordinate is \(2\), so \(P_4(2, 5.5)\) is farthest west. 4. The least y-coordinate is \(2\), so \(P_1(4.5, 2)\) is farthest south.

Answer

a) \(P_2(12, 6.5)\) b) \(P_3(7, 9)\) c) \(P_4(2, 5.5)\) d) \(P_1(4.5, 2)\)
Plot and interpret points 10
A theme park map shows several attractions on a coordinate grid: - \(R\): Ferris wheel - \(A\): roller coaster - \(K\): carousel - \(G\): haunted house - \(S\): swinging ship Use the map to answer each question. a) Which attraction is located at \((5, 2)\)? b) What are the coordinates of the haunted house, \(G\)?
Figure for problem 532172

Hints

- Read the x-coordinate before the y-coordinate. - The first coordinate gives the horizontal position. - The second coordinate gives the vertical position.

Solution

1. The point at \((5, 2)\) is labeled \(A\), so it represents the roller coaster. 2. Point \(G\) is \(3\) units right and \(1\) unit up from the origin, so its coordinates are \((3, 1)\).

Answer

a) The roller coaster, point \(A\) b) \((3, 1)\)
Plot and interpret points 11
Five points, \(A\), \(B\), \(C\), \(D\), and \(E\), are shown on a coordinate grid. a) What are the coordinates of point \(A\)? b) Which point is located at \((4, 2)\)? c) Start at point \(B\). Move \(2\) units left and \(3\) units up. Which labeled point do you reach?
Figure for problem 532176

Hints

- Read the horizontal coordinate before the vertical coordinate. - Think about how a leftward move changes a point's position. - Think about how an upward move changes a point's position.

Solution

1. Point \(A\) has x-coordinate \(1\) and y-coordinate \(4\), so \(A=(1, 4)\). 2. The point at \((4, 2)\) is \(B\). 3. Starting at \(B(4, 2)\), moving \(2\) units left and \(3\) units up gives \((4-2, 2+3)=(2, 5)\), which is point \(D\).

Answer

a) \((1, 4)\) b) \(B\) c) \(D\)
Plot and interpret points 12
On a neighborhood map, the first coordinate tells how many blocks east a place is from the starting corner, and the second coordinate tells how many blocks north it is. The community center is at \(C(5, 3)\). a) What does the \(5\) mean? b) What does the \(3\) mean? c) A playground is at \((5, 7)\). How is its east-west position related to the community center's position?

Hints

- Match each coordinate with the direction named in the map description. - Read the ordered pair in its given order. - Compare the first coordinates in part c).

Solution

1. The first coordinate is the east-west position, so \(5\) means the community center is \(5\) blocks east of the starting corner. 2. The second coordinate is the north-south position, so \(3\) means it is \(3\) blocks north. 3. The playground also has first coordinate \(5\), so it is the same distance east as the community center.

Answer

a) \(5\) blocks east b) \(3\) blocks north c) They have the same east-west position.
Plot and interpret points 13
A coordinate map shows a library \(L\) and a school \(S\). Each coordinate unit represents one city block east or north from the starting corner. a) What are the coordinates of the library? b) How many blocks east and north is the library from the starting corner? c) Which place is farther east, the library or the school?
Figure for problem 550478

Hints

- Read the library's horizontal and vertical positions from the axes. - Connect the first coordinate with east-west position. - Compare horizontal coordinates for part c).

Solution

1. The library is plotted at \((3, 5)\). 2. This means it is \(3\) blocks east and \(5\) blocks north of the starting corner. 3. The school has x-coordinate \(7\), which is greater than the library's x-coordinate \(3\), so the school is farther east.

Answer

a) \((3, 5)\) b) \(3\) blocks east and \(5\) blocks north c) The school
Plot and interpret points 14
Four labeled points are shown on the coordinate plane. Start at point \(A\). Move \(3\) units right and then \(4\) units up. Which labeled point do you reach?
Figure for problem 550479

Hints

- Track the horizontal move before the vertical move. - Change only one coordinate for each move. - Match the endpoint to the labels on the graph.

Solution

1. Point \(A\) is at \((2, 2)\). 2. Moving \(3\) units right gives \((5, 2)\). 3. Moving \(4\) units up gives \((5, 6)\), which is point \(C\).

Answer

\(C\)
Plot and interpret points 15
Point \(A\) is at \((3, 7)\). Point \(B\) has coordinates \((8, y)\) and lies on the same horizontal line as \(A\). What is the value of \(y\)?

Hints

- Picture two points lined up left to right. - Decide which part of their ordered pairs must match. - Use the known coordinate from point \(A\).

Solution

1. Points on the same horizontal line have the same y-coordinate. 2. Point \(A\) has y-coordinate \(7\), so \(B\) must also have y-coordinate \(7\). 3. Therefore, \(y=7\).

Answer

\(y=7\)
Plot and interpret points 16
Point \(C\) is at \((6, 2)\). Point \(D\) has coordinates \((x, 9)\) and lies on the same vertical line as \(C\). What is the value of \(x\)?

Hints

- Picture two points lined up above and below each other. - Decide which part of their ordered pairs must match. - Use the known coordinate from point \(C\).

Solution

1. Points on the same vertical line have the same x-coordinate. 2. Point \(C\) has x-coordinate \(6\), so point \(D\) must also have x-coordinate \(6\). 3. Therefore, \(x=6\).

Answer

\(x=6\)
Plot and interpret points 17
Four points are shown on the coordinate plane. a) Which point is farthest to the right? b) Which point is highest? c) Explain which coordinate you compared for each question.
Figure for problem 550482

Hints

- Separate the question about horizontal position from the question about vertical position. - Use one coordinate for left-right comparisons. - Use the other coordinate for up-down comparisons.

Solution

1. The x-coordinates are \(1, 5, 4,\) and \(7\). The greatest is \(7\), so point \(D\) is farthest to the right. 2. The y-coordinates are \(6, 3, 7,\) and \(5\). The greatest is \(7\), so point \(C\) is highest. 3. Horizontal position is compared with x-coordinates; vertical position is compared with y-coordinates.

Answer

a) \(D\) b) \(C\) c) Compare x-coordinates for rightmost position and y-coordinates for highest position.
Plot and interpret points 18
On a park map, locations are measured in blocks east and north from the entrance. A garden is \(4\) blocks east and \(6\) blocks north of the entrance. a) Write the garden's location as an ordered pair. b) A fountain is at the same east-west position as the garden but \(2\) blocks farther south. What are the fountain's coordinates?

Hints

- Translate the east and north distances into the two parts of an ordered pair. - Decide which coordinate stays fixed when two places have the same east-west position. - A southward move lowers one coordinate.

Solution

1. The first coordinate gives blocks east and the second gives blocks north, so the garden is at \((4, 6)\). 2. The fountain keeps x-coordinate \(4\). Moving \(2\) blocks south changes the y-coordinate from \(6\) to \(4\). 3. The fountain is at \((4, 4)\).

Answer

a) \((4, 6)\) b) \((4, 4)\)
Plot and interpret points 19
From left to right, the plotted points represent positions \(1\) through \(4\) in two patterns. What are the Pattern A and Pattern B terms at position \(3\)? Write them as the ordered pair \((\text{Pattern A}, \text{Pattern B})\).
Figure for problem 550998

Hints

- Count the plotted points from left to right to locate position \(3\). - Read the x-coordinate and y-coordinate of that point. - Keep Pattern A first when writing the ordered pair.

Solution

1. The third plotted point from the left has x-coordinate \(6\) and y-coordinate \(9\). 2. The position-\(3\) terms are \(6\) in Pattern A and \(9\) in Pattern B. 3. The ordered pair is \((6, 9)\).

Answer

Pattern A term: \(6\) Pattern B term: \(9\) Ordered pair: \((6, 9)\)
Plot and interpret points 20
A board-game token starts at point A. It moves \(4\) spaces to the right without moving up or down. Each small grid space represents \(1\) space, and the numbered tick marks are \(2\) spaces apart. a) Which labeled point is the token's new position? b) What are the coordinates of that point? c) Which coordinate stayed the same during the move?
Figure for problem 559057

Hints

- Start by reading the coordinates of point A from the grid. - Think about what a horizontal move changes on a coordinate plane. - Use the move size to find the new horizontal coordinate, then match it to a labeled point.

Solution

1. Point A is at \((3, 6)\). 2. Moving \(4\) spaces to the right changes the x-coordinate from \(3\) to \(7\) and leaves the y-coordinate at \(6\). 3. The new position is \((7, 6)\), which is point C. 4. The y-coordinate stayed the same.

Answer

a) C b) \((7, 6)\) c) The y-coordinate stayed the same.
Plot and interpret points 21
A campground map uses coordinates in hundreds of feet east and north from the ranger station. - Cabin A: \((2, 7)\) - Cabin B: \((6, 7)\) - Cabin C: \((6, 3)\) - Cabin D: \((4, 5)\) a) Which cabins are the same distance north of the ranger station? b) Which two cabins are directly above and below each other? c) How far apart are Cabin B and Cabin C in the north-south direction?

Hints

- Compare coordinates that represent north-south position for part a). - Directly above and below means the east-west position does not change. - Use the map's scale after finding the coordinate difference.

Solution

1. Cabins A and B both have y-coordinate \(7\), so they are the same distance north. 2. Cabins B and C both have x-coordinate \(6\), so they are directly above and below each other. 3. Their y-coordinates differ by \(7-3=4\) coordinate units. Each unit is \(100\) feet, so they are \(400\) feet apart north to south.

Answer

a) Cabins A and B b) Cabins B and C c) \(400\,\text{ft}\)
Plot and interpret points 22
Ivana was asked to plot point \(T(4, 6)\). The graph shows Ivana's plotted point \(T\). a) What coordinates are actually shown? b) Is the x-coordinate correct, the y-coordinate correct, both, or neither? c) Describe how to correct the plotted point.
Figure for problem 550485

Hints

- Read the plotted point before comparing it with the requested ordered pair. - Compare the two coordinates one at a time. - Decide which direction changes only the incorrect coordinate.

Solution

1. The shown point is at \((4, 5)\). 2. Its x-coordinate \(4\) is correct, but its y-coordinate should be \(6\), not \(5\). 3. Move the point \(1\) unit up to \((4, 6)\).

Answer

a) \((4, 5)\) b) The x-coordinate is correct; the y-coordinate is not. c) Move \(T\) \(1\) unit up to \((4, 6)\).
Plot and interpret points 23
Start at \(P(2, 3)\). Move \(4\) units right, then \(2\) units up, then \(1\) unit left. a) What are the coordinates after the first move and after the second move? b) What are the coordinates of the final point after the third move?

Hints

- Handle one move at a time instead of combining them immediately. - A horizontal move changes one coordinate, while a vertical move changes the other. - Check the direction of the final move before finding part b).

Solution

1. After moving \(4\) units right, the point is \((6, 3)\). 2. After moving \(2\) units up, the point is \((6, 5)\). 3. After moving \(1\) unit left, the final point is \((5, 5)\).

Answer

a) \((6, 3)\), then \((6, 5)\) b) \((5, 5)\)
Plot and interpret points 24
Point \(A\) is shown, point \(B\) is shown, and two dashed guide segments meet at point \(P\). Point \(P\) is directly to the right of \(A\) and directly above \(B\). What are the coordinates of \(P\)? Explain how the two alignments determine its coordinates.
Figure for problem 550487

Hints

- Use the horizontal guide to determine one coordinate. - Use the vertical guide to determine the other coordinate. - Combine one coordinate from each labeled point.

Solution

1. Point \(A\) is at \((2, 6)\). Because \(P\) is directly to the right of \(A\), \(P\) has y-coordinate \(6\). 2. Point \(B\) is at \((7, 3)\). Because \(P\) is directly above \(B\), \(P\) has x-coordinate \(7\). 3. Therefore, \(P=(7, 6)\).

Answer

\(P(7, 6)\)
Plot and interpret points 25
Two students start at \(S(2, 2)\). - Route A: move \(3\) units right, \(4\) units up, then \(1\) unit left. - Route B: move \(2\) units right, then \(4\) units up. Do the two routes end at the same point? Show the endpoint of each route.

Hints

- Track each route independently from the same starting point. - Record the ordered pair after every move. - Compare the two final ordered pairs rather than the route lengths.

Solution

1. Route A goes from \((2, 2)\) to \((5, 2)\), then \((5, 6)\), then \((4, 6)\). 2. Route B goes from \((2, 2)\) to \((4, 2)\), then \((4, 6)\). 3. Both routes end at \((4, 6)\), so they reach the same point.

Answer

Yes. Both routes end at \((4, 6)\).
Plot and interpret points 26
A meeting station has whole-number coordinates. - It lies on the same horizontal line as \(A(2, 7)\). - It lies strictly between the vertical line through \(B(6, 3)\) and the vertical line through \(C(9, 4)\). - It is closer to the vertical line through \(C\) than to the vertical line through \(B\). What are the station's coordinates? Explain how each condition narrows the possibilities.

Hints

- First use the horizontal-line condition to determine one coordinate. - Then list the whole-number x-positions strictly between the two vertical lines. - Compare each remaining position's horizontal distance to the two vertical lines.

Solution

1. The same horizontal line as \(A(2, 7)\) gives y-coordinate \(7\). 2. The station lies strictly between the vertical lines \(x=6\) and \(x=9\). With a whole-number x-coordinate, the possibilities are \(7\) and \(8\). 3. At \(x=7\), the station is \(1\) unit from \(x=6\) and \(2\) units from \(x=9\), so it is closer to \(B\)'s vertical line. 4. At \(x=8\), it is \(2\) units from \(x=6\) and \(1\) unit from \(x=9\), so it is closer to \(C\)'s vertical line. 5. Therefore, the station is at \((8, 7)\).

Answer

\((8, 7)\)
Plot and interpret points 27
Three panels show attempts to plot the same four points: \(A(1, 2)\), \(B(1, 6)\), \(C(5, 6)\), and \(D(7, 3)\). a) Which panel shows all four points plotted correctly? b) For each incorrect panel, identify the misplaced point and give the coordinates actually shown for it.
Figure for problem 554298

Hints

- Check each labeled point against its ordered pair one coordinate at a time. - Do not decide from the overall shape of the four points. - In an incorrect panel, read the misplaced point's actual x- and y-coordinates from the axes.

Solution

1. In panel a), \(A\), \(B\), \(C\), and \(D\) are all at their stated ordered pairs. 2. In panel b), \(A\) is shown at \((2, 1)\) instead of \((1, 2)\). The other three points are correctly placed. 3. In panel c), \(C\) is shown at \((6, 5)\) instead of \((5, 6)\). The other three points are correctly placed. 4. Therefore, panel a) is the correct plot.

Answer

a) Panel a) b) Panel b): \(A\) is shown at \((2, 1)\). Panel c): \(C\) is shown at \((6, 5)\).
Plot and interpret points 28
Linh tried to plot \(U(4, 2)\), \(V(8, 6)\), and \(W(2, 8)\). On the graph, numbered tick labels increase by \(2\), while each small grid space represents \(1\) unit. a) Which labeled points are plotted correctly? b) Which point is misplaced? Give the coordinates where it is actually shown and the coordinates where it should be.
Figure for problem 554299

Hints

- Use the numbered tick values rather than counting labeled intervals as single units. - Read the x-coordinate and y-coordinate of each shown point separately. - Compare each shown ordered pair with the target ordered pair in the text.

Solution

1. Read positions from the numbered axes while remembering that each small grid space is \(1\) unit. 2. \(U\) is shown at \((4, 2)\), so \(U\) is correct. 3. \(W\) is shown at \((2, 8)\), so \(W\) is correct. 4. \(V\) is shown at \((4, 3)\), not \((8, 6)\). 5. Therefore, \(V\) is the misplaced point and should be moved to \((8, 6)\).

Answer

a) \(U\) and \(W\) b) \(V\) is shown at \((4, 3)\) and should be at \((8, 6)\).
Plot and interpret points 29
Riverside Science Club records how much water has collected after a faucet is turned on. <table> <tr><th>Record</th><th>Time after start (minutes)</th><th>Water collected (liters)</th></tr> <tr><td>A</td><td>1</td><td>2</td></tr> <tr><td>B</td><td>2</td><td>3</td></tr> <tr><td>C</td><td>3</td><td>5</td></tr> <tr><td>D</td><td>4</td><td>8</td></tr> </table> The graph shows Haruki's plot of records A–D. a) Which plotted record does not match the table? b) What coordinates should that point have? c) What does the corrected point mean in this situation?
Figure for problem 554300

Hints

- Match each graph label with the table row carrying the same letter. - For each record, time is the x-coordinate and water collected is the y-coordinate. - After finding the mismatch, interpret the corrected ordered pair using the axis meanings.

Solution

1. Compare each table row with the plotted point carrying the same letter. 2. A is plotted at \((1, 2)\), B at \((2, 3)\), and D at \((4, 8)\), matching the table. 3. C is plotted at \((3, 4)\), but the table gives time \(3\) and water \(5\). 4. Therefore, C should be at \((3, 5)\). 5. The corrected point means that after \(3\) minutes, \(5\,\text{liters}\) of water had collected.

Answer

a) Record C b) \((3, 5)\) c) After \(3\) minutes, \(5\,\text{liters}\) of water had collected.

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