8th Grade Distance on the Coordinate Plane Worksheet Solutions (PDF)
This distance coordinate plane answers for 8th Grade covers distance on the coordinate plane (Common Core 8.G.B.8), with a free PDF to print.
This answer key gives a full worked solution for each of the 20 problems on the distance on the coordinate plane worksheet (Common Core 8.G.B.8). Compare each step with your own work, not only the final answer, and note any step where your method differed.
Grade 8 · Common Core State Standards: 8.G.B.8
Distance coordinate plane answers: exercises 1 to 10
Exercise 1 – Distance with a triangle
Legs: \(4 – (-1) = 5\) and \(14 – 2 = 12\).
\(d = \sqrt{25 + 144} = 13\).
13
Exercise 2 – From the origin
\(d = \sqrt{5^{2} + 12^{2}} = \sqrt{169} = 13\).
13
Exercise 3 – Negative coordinates
Legs: \(5 – (-3) = 8\) and \(7 – 1 = 6\).
\(d = \sqrt{64 + 36} = 10\).
10
Exercise 4 – Larger numbers
Legs: 5 and \(8 – (-4) = 12\).
\(d = \sqrt{25 + 144} = 13\).
13
Exercise 5 – Not a whole number
Legs: 6 and 2.
\(d = \sqrt{36 + 4} = \sqrt{40} \approx 6.3\).
about 6.3
Exercise 6 – Horizontal segment
The points have the same y-coordinate, so subtract: \(6 – (-4) = 10\).
10
Exercise 7 – Vertical segment
\(4 – (-5) = 9\).
9
Exercise 8 – Triangle perimeter
\(AB = 6\), \(AC = 8\), \(BC = \sqrt{36 + 64} = 10\).
24
Exercise 9 – Right triangle test
Sides: 3 (horizontal), 4 (vertical), and \(\sqrt{9 + 16} = 5\). Also \(3^{2} + 4^{2} = 5^{2}\).
Yes
Exercise 10 – Closer point
\(\sqrt{9 + 25} = \sqrt{34} \approx 5.83\) and \(\sqrt{16 + 16} = \sqrt{32} \approx 5.66\).
\((4, 4)\) is closer
Exercises 11 and up
Exercise 11 – Rhombus perimeter
\(AB = \sqrt{9 + 16} = 5\), \(BC = 5\), \(CD = \sqrt{9 + 16} = 5\), \(DA = 5\).
20
Exercise 12 – Find the missing coordinate
\(36 + y^{2} = 100\), so \(y^{2} = 64\).
\(y = 8 \text{ or } y = -8\)
Exercise 13 – Rectangle diagonal
Legs: 6 and 8.
\(d = \sqrt{36 + 64} = 10\).
10
Exercise 14 – Drone flight
Legs: 9 and 12.
\(d = \sqrt{81 + 144} = 15\).
15 miles
Exercise 15 – Two cities
Legs: \(6 – (-9) = 15\) and \(4 – (-4) = 8\).
\(d = \sqrt{225 + 64} = \sqrt{289} = 17\).
17 miles
Exercise 16 – Walk to the library
\(d = \sqrt{64 + 225} = 17\).
17 blocks
Exercise 17 – Robot path
Legs: 5 and 12.
\(d = \sqrt{25 + 144} = 13\).
13 feet
Exercise 18 – Compare routes
Two legs: \(9 + 12 = 21\). Direct: \(\sqrt{81 + 144} = 15\).
6 units shorter
Exercise 19 – Zip line
Legs: 16 and 12.
\(d = \sqrt{256 + 144} = \sqrt{400} = 20\).
20 feet
Exercise 20 – Explain the formula
The change in x and the change in y are the legs of a right triangle, and the distance is the hypotenuse.
\(d^{2} = (\Delta x)^{2} + (\Delta y)^{2}\)
Key facts behind this distance coordinate plane answers
- 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 answers
Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.
All Grade 8 chapters: Grade 8 math.
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