Grade 8 · Math

8th grade Distance between two points on the grid worksheet

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Distance between two points on the grid

Grade 8 Math Worksheet - Challenge Me

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Circle the best answer, or write your answer on the line.

Pia's grid shows a triangle-shaped flower bed with corners (-3, -4), (4, -4) and (4, 3). To the nearest tenth of a unit, what is its perimeter?
Ren's grid shows a paper triangle on grid paper with corners (-5, -2), (3, -2) and (3, 8). To the nearest tenth of a unit, what is its perimeter?
Zee's grid shows a triangle kite frame with corners (-8, 1), (-5, 1) and (-5, 10). To the nearest tenth of a unit, what is its perimeter?
4.
Ari plots a triangle at (0, 0), (2, 1) and (1, 3). Is it a right triangle?
- You cannot tell without measuring the angles.
- No, it is not a right triangle: the squares of the two shorter sides do not add up to the square of the longest.
- Yes, it is a right triangle, because two of its sides slant.
- Yes, it is a right triangle: the squares of the two shorter sides add up to the square of the longest.
5.
Bo's robot marks the corners (-2, 1), (1, 3) and (3, 0). Is the triangle a right triangle?
- No, it is not a right triangle: the squares of the two shorter sides do not add up to the square of the longest.
- Yes, it is a right triangle, because two of its sides slant.
- You cannot tell without measuring the angles.
- Yes, it is a right triangle: the squares of the two shorter sides add up to the square of the longest.
6.
Esme draws a triangle with corners (0, 0), (3, 1) and (1, 4) in pencil. Is it a right triangle?
- No, it is not a right triangle: the squares of the two shorter sides do not add up to the square of the longest.
- Yes, it is a right triangle: the squares of the two shorter sides add up to the square of the longest, so it has a square corner.
- You cannot tell without measuring the angles.
- Yes, it is a right triangle, because two of its sides slant.
7.
On a grid map, Jun joins (-3, 0), (1, 2) and (2, -1). Is the triangle a right triangle?
- Yes, it is a right triangle, because two of its sides slant.
- You cannot tell without measuring the angles.
- Yes, it is a right triangle: the squares of the two shorter sides add up to the square of the longest.
- No, it is not a right triangle: the squares of the two shorter sides do not add up to the square of the longest.
On Luz's map, each square is one km across. The harbor is at (-3, 2) and the island is at (1, 7). To the nearest tenth of a km, how far apart are they?
On Milo's map, each square is one km across. The depot is at (-5, -3) and the museum is at (1, 3). To the nearest tenth of a km, how far apart are they?
On Noah's map, each square is one km across. The trailhead is at (-1, -4) and the bridge is at (1, -1). To the nearest tenth of a km, how far apart are they?

8th grade Distance between two points on the grid worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Distance between two points on the grid. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can draw the right triangle under a slanted segment and count its legs, even across zero.
I can find the distance between two points as the side of the square on the segment: an exact root or to the nearest tenth.
I can compare two distances, find a perimeter with a slanted side, and test whether a triangle on the grid is a right triangle.

Standard: 8.G.B.8

Words to know

segment: The straight piece of line between two points.

leg (across, up or down): A side of the right triangle that runs along a grid line.

right-angle corner: Where the across leg meets the up-or-down leg.

distance: How long the straight segment is: the side of its square.

across zero: From a negative number to a positive one: add the two parts.

Common mistakes

Your child subtracted the sizes of two coordinates that sit on opposite sides of zero. Going from -3 to 5 is 3 units to zero and 5 more: 8 in all. Count the squares on the grid together.

Your child counted the wrong leg of the triangle. 'Across' is the change in x, the first numbers; 'up or down' is the change in y, the second numbers.

Your child added the two legs of the triangle to get the slanted distance. The squares on the legs add up to the square on the slanted side; the lengths do not. Try legs of 3 and 4: the slanted side is 5, not 7.

Questions parents ask

What is the most common mistake with distance between two points on the grid?

Your child subtracted the sizes of two coordinates that sit on opposite sides of zero. Going from -3 to 5 is 3 units to zero and 5 more: 8 in all. Count the squares on the grid together.

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

See all grade 8 math

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