This grade 8 distance worksheet answer key solves all 24 problems of the distance in the coordinate plane worksheet step by step.
Each solution finds the horizontal and vertical legs first, squares them, adds, and takes the square root. Rounded answers are given to the nearest tenth. When an answer differs, recheck the signs of the subtraction, since the absolute value of each leg is what matters.
Grade 8 Distance Worksheet Answer Key: problems 1–5
Problem 1: Horizontal distance
Both points have \(y=5\), so the segment is horizontal. \(|9-2|=7\).
The distance is 7 units.
Problem 2: Vertical distance
Both points have \(x=-3\), so the segment is vertical. \(|6-(-4)|=10\).
The distance is 10 units.
Problem 3: Draw the legs
Horizontal leg: \(4-1=3\). Vertical leg: \(5-1=4\). Then \(d^{2}=3^{2}+4^{2}=9+16=25\).
\(AB=\)5 units.
Problem 4: Distance from the origin
The legs are 5 and 12. \(d^{2}=5^{2}+12^{2}=25+144=169\).
\(d=\)13 units.
Problem 5: Two points in Quadrant I
Legs: \(10-2=8\) and \(9-3=6\). \(d^{2}=64+36=100\).
\(d=\)10 units.
Grade 8 Distance Worksheet Answer Key: problems 6–10
Problem 6: Across quadrants
Legs: \(4-(-2)=6\) and \(7-(-1)=8\). \(d^{2}=36+64=100\).
\(d=\)10 units.
Problem 7: Moving down and right
Legs: \(5-(-7)=12\) and \(|-2-3|=5\). \(d^{2}=144+25=169\).
\(d=\)13 units.
Problem 8: Distance that is not whole
Legs: \(5-1=4\) and \(6-1=5\). \(d^{2}=16+25=41\), so \(d=\sqrt{41}\).
\(\sqrt{41}\approx 6.40\), so the distance is about 6.4 units.
Problem 9: Larger legs
Legs: \(2-(-3)=5\) and \(|-6-4|=10\). \(d^{2}=25+100=125\).
\(d=\sqrt{125}\approx 11.18\), so the distance is about 11.2 units.
Problem 10: Use the distance formula
\(d=\sqrt{(7-(-8))^{2}+(5-(-3))^{2}}=\sqrt{15^{2}+8^{2}}=\sqrt{225+64}=\sqrt{289}\).
\(d=\)17 units.
Grade 8 Distance Worksheet Answer Key: problems 11–15
Problem 11: Find the error
Liam added the legs. The distance is the hypotenuse, so the legs must be squared, added, and then the square root is taken.
\(d^{2}=3^{2}+4^{2}=25\), so \(d=5\). The distance is 5 units, not 7.
Problem 12: Which point is closer?
\(OP=\sqrt{5^{2}+(-6)^{2}}=\sqrt{61}\approx 7.8\). \(OQ=\sqrt{(-7)^{2}+3^{2}}=\sqrt{58}\approx 7.6\).
Since 58 is less than 61, point \(Q\) is closer to the origin.
Problem 13: Missing coordinate
The horizontal leg is \(7-1=6\). So \(6^{2}+(y-2)^{2}=10^{2}\), which gives \((y-2)^{2}=100-36=64\).
Then \(y-2=8\), so \(y=10\).
Problem 14: Perimeter of a grid triangle
Bottom side: 6. Right side: 8. Slanted side: \(\sqrt{6^{2}+8^{2}}=\sqrt{100}=10\).
Perimeter: \(6+8+10=\)24 units.
Problem 15: Perimeter of a rhombus
Each side has legs 4 and 3, so each side is \(\sqrt{4^{2}+3^{2}}=\sqrt{25}=5\).
All four sides are 5, so the perimeter is \(4\cdot 5=\)20 units.
Grade 8 Distance Worksheet Answer Key: problems 16–20
Problem 16: Perimeter with a slanted side
Horizontal side: \(2-(-4)=6\). Vertical side: \(3-0=3\). Slanted side: \(\sqrt{6^{2}+3^{2}}=\sqrt{45}\approx 6.71\).
Perimeter: \(6+3+6.71\approx\)15.7 units.
Problem 17: Is the triangle isosceles?
\(AB=|5-1|=4\). \(AC=\sqrt{2^{2}+4^{2}}=\sqrt{20}\). \(BC=\sqrt{(-2)^{2}+4^{2}}=\sqrt{20}\).
Two sides have the same length \(\sqrt{20}\approx 4.5\), so the triangle is isosceles.
Problem 18: Is the triangle a right triangle?
\(AB^{2}=3^{2}+4^{2}=25\). \(BC^{2}=4^{2}+(-3)^{2}=25\). \(AC^{2}=7^{2}+1^{2}=50\).
Check the converse: \(AB^{2}+BC^{2}=25+25=50=AC^{2}\), so the triangle is a right triangle with the right angle at \(B\).
Problem 19: Library to park
Legs: \(8-2=6\) miles and \(11-3=8\) miles. \(d^{2}=36+64=100\).
They are 10 miles apart.
Problem 20: Drone flight
Legs: \(8-(-4)=12\) and \(2-(-3)=5\). \(d^{2}=144+25=169\).
The drone flies 13 yards.
Grade 8 Distance Worksheet Answer Key: problems 21–24
Problem 21: Home to school
Legs: \(6-(-3)=9\) and \(|-10-2|=12\). \(d^{2}=81+144=225\), so \(d=15\) units.
Each unit is 0.1 mile: \(15\times 0.1=\)1.5 miles.
Problem 22: Fence for a garden
Sides: \(9\) ft, \(12\) ft and \(\sqrt{9^{2}+12^{2}}=\sqrt{225}=15\) ft. Perimeter: \(9+12+15=36\) ft.
Cost: \(36\times 3.50=\)\$126.
Problem 23: Jogging loop
Two sides are 5 blocks. The slanted side is \(\sqrt{5^{2}+5^{2}}=\sqrt{50}\approx 7.07\).
Loop: \(5+5+7.07\approx\)17.1 blocks.
Problem 24: Video game character
Legs: \(6-(-6)=12\) and \(3-(-2)=5\). \(d^{2}=144+25=169\), so \(d=13\) units.
Time: \(13: 2.6=\)5 seconds.
How to use this grade 8 distance worksheet answer key
Read this grade 8 distance worksheet answer key after trying each problem yourself, and redo any problem you missed.
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Grade 8 Distance in the Coordinate Plane worksheet answer key
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