Distance in the Coordinate Plane: Grade 8 Math Test Answer Key – PDF Download

Question 1: Horizontal and vertical distance (2 points)

1. \(|5-(-4)|=\)9 units.
2. \(|8-(-6)|=\)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)

1. \(DE=|1-(-4)|=5\). \(EF=|1-(-2)|=3\). \(DF=\sqrt{5^{2}+3^{2}}=\sqrt{34}\approx 5.8\).
2. 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.

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)

1. Legs: \(7-(-5)=12\) and \(2-(-3)=5\). \(d^{2}=144+25=169\), so \(d=13\) units. \(13\times 0.1=\)1.3 miles.
2. \(1.3: 6.5=0.2\) 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.

⬇ Download the Grade 8 Distance in the Coordinate Plane test answer key (PDF, 103 KB)

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