8th Grade Distance on the Coordinate Plane Test with Point Values (PDF)

8th Grade math test: Distance on the Coordinate Plane – Maths PDF

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This distance coordinate plane test for 8th Grade covers distance on the coordinate plane (Common Core 8.G.B.8), with a free PDF to print.

This 20-point test checks the distance formula on the coordinate plane, perimeters of figures and map problems (Common Core 8.G.B.8). Work alone, show every step, and write each final answer clearly. You have 45 minutes. Calculators are not needed unless a question says so.

Time and points

About this test

Grade: Grade 8
Chapter: Distance on the Coordinate Plane
Standards: 8.G.B.8
Time: 45 minutes
Total: 20 points

Distance coordinate plane test: questions

Question 1 – Distance [3 pts]

Find AB.

Find the distance between \(A(1, 1)\) and \(B(7, 9)\).

Question 2 – Estimate [2 pts]

Find the distance between \((-1, 2)\) and \((4, 5)\) to the nearest tenth.

Question 3 – Perimeter [3 pts]

Triangle ABC.

Find the perimeter of triangle \(ABC\) with \(A(0, 0)\), \(B(9, 0)\), \(C(0, 12)\).

Question 4 – Right triangle? [3 pts]

Is the triangle with vertices \((0, 0)\), \((5, 0)\) and \((5, 12)\) a right triangle? Find all three side lengths.

Question 5 – Missing coordinate [2 pts]

The distance from \((0, 0)\) to \((x, 12)\) is 13, with \(x > 0\). Find \(x\).

Question 6 – Map problem [3 pts]

Home H and school S, in blocks.

On a city map, a student’s home is at \(H(0, 0)\) and the school is at \(S(15, 8)\), with each unit a block. How many blocks is it in a straight line? How many blocks shorter is that than walking along the streets (east then north)?

Question 7 – Compare distances [2 pts]

Which is farther from the origin, \((6, 8)\) or \((7, 7)\)? Show your work.

Question 8 – Explain [2 pts]

Why is subtracting the coordinates enough for a horizontal segment, but not for a slanted one?

Key facts behind this distance coordinate plane test

Key facts

Distance: \(d = \sqrt{(x_{2} – x_{1})^{2} + (y_{2} – y_{1})^{2}}\).
The horizontal and vertical changes are the legs of a right triangle.
For horizontal or vertical segments, just subtract coordinates.
Perimeter: find each side with the distance formula and add.
Distances can be whole numbers or square roots to estimate.

How to use this distance coordinate plane test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 8 chapters: Grade 8 math.

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