This grade 8 distance test answer key gives the full solution and the scoring guide for each of the 8 test questions on distance in the coordinate plane.
Use this key to score the coordinate distance test out of 20 points. Each solution shows the legs, the squares and the square root, and the scoring note explains the partial credit. Accept equivalent exact forms such as \(\sqrt{45}\) when no rounding is requested.
Grade 8 Distance Test Answer Key: questions 1–5
Question 1: Horizontal and vertical distance (2 points)
- \(|5-(-4)|=\)9 units.
- \(|8-(-6)|=\)14 units.
Scoring: 1 point for each correct distance.
Question 2: Distance between two points (2 points)
Legs: \(5-(-3)=8\) and \(4-(-2)=6\). \(d^{2}=64+36=100\), so \(d=10\) units.
Scoring: 1 point for the two legs and the sum of squares, 1 point for 10.
Question 3: Rounded distance (2 points)
Legs: \(7-1=6\) and \(|-1-(-4)|=3\). \(d^{2}=36+9=45\), so \(d=\sqrt{45}\approx 6.7\) units.
The distance is about 6.7 units.
Scoring: 1 point for \(d^{2}=45\), 1 point for the rounded distance.
Question 4: Perimeter of a triangle (3 points)
- \(DE=|1-(-4)|=5\). \(EF=|1-(-2)|=3\). \(DF=\sqrt{5^{2}+3^{2}}=\sqrt{34}\approx 5.8\).
- Perimeter \(\approx 5+3+5.8=\)13.8 units.
Scoring: Part (a): 1 point for the two straight sides, 1 point for \(\sqrt{34}\). Part (b): 1 point.
Question 5: Is it a right triangle? (3 points)
\(JK^{2}=4^{2}+2^{2}=20\). \(JL^{2}=1^{2}+(-2)^{2}=5\). \(KL^{2}=(-3)^{2}+(-4)^{2}=25\).
The longest side is \(KL\), and \(JK^{2}+JL^{2}=20+5=25=KL^{2}\). By the converse of the Pythagorean Theorem, it is a right triangle with the right angle at \(J\).
Scoring: 1 point for the three squared lengths, 1 point for comparing with the longest side, 1 point for the conclusion.
Grade 8 Distance Test Answer Key: questions 6–8
Question 6: Missing coordinate (2 points)
The vertical leg is \(5-(-1)=6\). So \((x+2)^{2}+6^{2}=10^{2}\), and \((x+2)^{2}=64\).
Then \(x+2=8\), so \(x=6\).
Scoring: 1 point for the equation \((x+2)^{2}+36=100\), 1 point for \(x=6\).
Question 7: Perimeter of a trapezoid (3 points)
\(AB=8\) and \(CD=5-2=3\). \(BC=\sqrt{3^{2}+4^{2}}=5\). \(DA=\sqrt{2^{2}+4^{2}}=\sqrt{20}\approx 4.5\).
Perimeter: \(8+5+3+4.5=\)20.5 units.
Scoring: 1 point for the two straight sides (8 and 3), 1 point for the two slanted sides, 1 point for the perimeter.
Question 8: Bike to school (3 points)
- Legs: \(7-(-5)=12\) and \(2-(-3)=5\). \(d^{2}=144+25=169\), so \(d=13\) units. \(13\times 0.1=\)1.3 miles.
- \(1.3: 6.5=0.2\) hour, and \(0.2\times 60=\)12 minutes.
Scoring: Part (a): 1 point for 13 units, 1 point for converting to 1.3 miles. Part (b): 1 point.
Scoring summary
20 points: add the points of every question of this grade 8 distance test answer key.
How to use this grade 8 distance test answer key
Use this grade 8 distance test answer key to score the test fairly and to see which skills need more practice.
Printable PDF · Test Answer Key
Grade 8 Distance in the Coordinate Plane test answer key
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