Solve the problem.
-Decide whether or not the points are the vertices of a right triangle. (-9, 8), (-3, 10), (-4, 5)
A) No
B) Yes

Question

Quizplus · Accepted Answer

To determine if the points form a right triangle, calculate the distances between the points (sides of the triangle) and then check if the Pythagorean theorem holds for any two sides squared equaling the square of the third side (the longest). The distances between the points are: d1 = sqrt[(-3 + 9)^2 + (10 - 8)^2] = sqrt[36 + 4] = sqrt[40], d2 = sqrt[(-4 + 3)^2 + (5 - 10)^2] = sqrt[1 + 25] = sqrt[26], and d3 = sqrt[(-9 + 4)^2 + (8 - 5)^2] = sqrt[25 + 9] = sqrt[34]. None of these distances squared sum up to equal the square of the third distance, meaning they do not satisfy the Pythagorean theorem, and thus the points do not form a right triangle.

Solve the Problem. -Decide Whether or Not the Points Are the Vertices of the Vertices