8th Grade Distance on the Coordinate Plane Test Solutions and Scoring (PDF)

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

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

Use this answer key to score the distance on the coordinate plane test out of 20 points. Each solution shows the full work and a scoring guide, so partial credit can be given fairly when a student shows correct steps but makes an arithmetic slip.

Grade 8 · Common Core State Standards: 8.G.B.8

Distance coordinate plane test answers: worked solutions

Question 1 – Distance [3 pts]

AB = 10.

Legs: 6 and 8; \(\sqrt{36 + 64} = 10\).

Scoring: 1 point for the legs, 1 point for the equation, 1 point for 10.

Question 2 – Estimate [2 pts]

Legs: 5 and 3. \(\sqrt{25 + 9} = \sqrt{34} \approx 5.8\).

Scoring: 1 point for the equation. 1 point for 5.8.

Question 3 – Perimeter [3 pts]

BC = 15.

\(AB = 9\), \(AC = 12\), \(BC = 15\). Perimeter: 36.

Scoring: 1 point for BC, 1 point for the sides, 1 point for 36.

Question 4 – Right triangle? [3 pts]

Sides: 5, 12 and \(\sqrt{25 + 144} = 13\). The horizontal and vertical sides meet at \((5, 0)\) at a right angle: yes.

Scoring: 1 point for the legs 5 and 12, 1 point for the hypotenuse 13, 1 point for yes with a reason.

Question 5 – Missing coordinate [2 pts]

\(x^{2} + 144 = 169\), so \(x^{2} = 25\) and \(x = 5\).

Scoring: 1 point for the equation. 1 point for 5.

Question 6 – Map problem [3 pts]

\(d = \sqrt{225 + 64} = 17\). Streets: \(15 + 8 = 23\). Difference: 6 blocks.

Scoring: 1 point for the legs, 1 point for 17, 1 point for 6 blocks.

Question 7 – Compare distances [2 pts]

\(\sqrt{100} = 10\) and \(\sqrt{98} \approx 9.9\). So \((6, 8)\) is farther.

Scoring: 1 point for each distance or squared distance, 1 point for the conclusion (2 points total).

Question 8 – Explain [2 pts]

A horizontal segment has no vertical change, so its length is the horizontal change. A slanted segment is the hypotenuse of a right triangle and needs the Pythagorean theorem.

Scoring: 1 point for each part.

Total score

Total

20 points

Key facts behind this distance coordinate plane test answers

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 answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 8 chapters: Grade 8 math.

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