Key takeaway: This grade 8 distance coordinate plane quiz has ten multiple-choice questions on horizontal distance, slanted distance, perimeter, and map scale. Pick one answer for each item, and then study the note beneath it. The explanations show the legs and the root, and they flag the tempting wrong choices. Teachers can use the set as a short check.
Several options add the legs instead of taking the root of the sum of squares. Spotting that slip helps on many items.
Ten multiple-choice questions on distance in the coordinate plane (8.G.B.8). Use legs, the Pythagorean Theorem and the distance formula to find lengths and perimeters. Choose the single best answer, then read the explanation to see which mistake each wrong choice matches.
🎉 Quiz complete!
Remember:
- Standard 8.G.B.8: apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
- The horizontal and vertical changes are the legs of a right triangle; the segment is the hypotenuse.
- Distance formula: \(d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\).
- The order of the points does not matter, because squares are never negative.
- Perimeter on a grid: find each side length, then add them.
How do you find the distances in the first questions?
The first item uses two points on a horizontal line, from (-3, 4) to (6, 4), so the distance is 9. The second uses A(1, 2) and B(4, 6), where the legs 3 and 4 give 5. A third pair, (-2, -3) and (6, 3), has legs 8 and 6, so it is 10. Another pair gives the square root of 45, which rounds to 6.7.
What does a grade 8 distance coordinate plane quiz ask about expressions?
One item asks which expression gives the distance between (2, 5) and (-4, 1). The answer subtracts in the same order inside each parenthesis: negative 4 minus 2, and 1 minus 5. Another asks for the point exactly 10 units from the origin, and (6, 8) works because 36 plus 64 equals 100.
How do perimeter and map items work?
The triangle with vertices (0, 0), (3, 0), and (3, 4) has sides 3, 4, and 5, so the perimeter is 12. On a map with 5 miles per unit, Towns A(2, 2) and B(8, 10) are 10 units apart, which is 50 miles. A tilted square with side 5 has perimeter 20.
How do you find a missing coordinate?
From (1, 1) to (13, y) the distance is 13, and the horizontal leg is 12. Therefore the vertical leg is 5, and y is 6. Write the equation first and solve second.
After the distance quiz
Redo each miss, and write the two legs before the root. Next, check your answer by squaring it and comparing with the sum of the squared legs. Finally, take the printable set and look for problems that resemble your errors.
See every chapter on the Grade 8 math page.
