Solve the problem.
-Decide whether or not the points are the vertices of a right triangle. (-9, -1), (-4, -1), (-4, 7)
A) No
B) Yes

Question

Quizplus · Accepted Answer

To determine if the points form a right triangle, we can calculate the distances between the points (sides of the triangle) and then apply the Pythagorean theorem. The distances between the points are as follows: 1. Distance between (-9, -1) and (-4, -1) is 5 units (horizontal line).2. Distance between (-4, -1) and (-4, 7) is 8 units (vertical line).3. Distance between (-9, -1) and (-4, 7) is the hypotenuse, which can be calculated using the distance formula: $\sqrt{(7 - (-1))^2 + (-4 - (-9))^2} = \sqrt{8^2 + 5^2} = \sqrt{64 + 25} = \sqrt{89}$.Since the squares of the lengths of the two shorter sides (5 and 8) add up to the square of the length of the longest side ($\sqrt{89}$), the triangle satisfies the Pythagorean theorem ($5^2 + 8^2 = 89$), indicating it is a right triangle.

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