Determine if the given points form the vertices of a right triangle.
-(-3, 5), (-1, 3), and (-4, 0)
A) No
B) Yes

Question

Quizplus · Accepted Answer

To determine if the given points form the vertices of a right triangle, we can use the distance formula to calculate the lengths of the sides and then apply the Pythagorean theorem. The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$.1. Distance between (-3, 5) and (-1, 3): $\sqrt{(-1+3)^2 + (3-5)^2} = \sqrt{4 + 4} = \sqrt{8}$2. Distance between (-3, 5) and (-4, 0): $\sqrt{(-4+3)^2 + (0-5)^2} = \sqrt{1 + 25} = \sqrt{26}$3. Distance between (-1, 3) and (-4, 0): $\sqrt{(-4+1)^2 + (0-3)^2} = \sqrt{9 + 9} = \sqrt{18}$For these lengths to form a right triangle, the square of the longest side should equal the sum of the squares of the other two sides. Checking this:$\sqrt{26}$ is the longest side, so we check if $\sqrt{26}^2 = \sqrt{8}^2 + \sqrt{18}^2$$26 \neq 8 + 18$Therefore, the given points do not form the vertices of a right triangle.

Determine If the Given Points Form the Vertices of a Right