The vertices of a triangle are given. Use the distance formula to find what kind of triangle each is. A sketch of the graph might be helpful. Note: An isosceles triangle has two equal sides. An equilateral triangle has three equal sides. A right triangle satisfies the Pythagorean Theorem.
(4, 8), (1, 6), (5, 0)
A) isosceles equilateral
B) isosceles right
C) right, not isosceles
D) equilateral
E) isosceles

Question

Quizplus · Accepted Answer

Using the distance formula, we can find that the side lengths are approximately 4.24, 8.94, and 7.81. To see if it is a right triangle, we can check if the sum of the squares of the two shorter sides is equal to the square of the longest side: $4.24^2 + 7.81^2 \approx 77.07$ and $8.94^2 \approx 79.98$. Since these are not equal, the triangle is not a right triangle. Additionally, none of the side lengths are equal, so the triangle is not isosceles or equilateral. Therefore, the triangle is right and not isosceles.

The Vertices of a Triangle Are Given