Decide whether or not the points are the vertices of a right triangle.
-(-6, -6), (0, -4), (6, -11)
A)Yes
B)No

Question

Quizplus · Accepted Answer

To determine if a triangle is a right triangle, we need to check if the square of the longest side is equal to the sum of the squares of the other two sides. Using the distance formula, we find that the distances between the points are:
√(36+4) ≈ 6.08   for (-6, -6) to (0, -4)
√(36+49) ≈ 9.22   for (-6, -6) to (6, -11)
√(81+49) = 10      for (0, -4) to (6, -11)
The longest side is between (-6, -6) and (6, -11), so we need to check if the square of 9.22 is equal to the sum of the squares of 6.08 and 10, but it is not. Therefore, the points do not form a right triangle. If we calculate the distance between each pair of points, we get: 
- Distance between (-6,-6) and (0,-4) is approximately 3.6. 
- Distance between (-6,-6) and (6,-11) is approximately 7.8.
- Distance between (0,-4) and (6,-11) is approximately 8.2. 
These distances do not satisfy the Pythagorean theorem, which states that for a right triangle, the square of the length of the hypotenuse (longest side) is equal to the sum of the squares of the lengths of the other two sides. Therefore, these points are not the vertices of a right triangle.

Decide Whether or Not the Points Are the Vertices of a Right