Question

consider the following points. (-9, 6), (9, 1) and (9, 6) step 1 of 2: determine whether or not the given points form a right triangle. if the triangle is not a right triangle, determine if it is isosceles or scalene. answer right triangle isosceles triangle scalene triangle

Explanation:

Step1: Calculate the distances between points

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let $A(-9,6)$, $B(9,1)$, $C(9,6)$.
The distance between $A(-9,6)$ and $B(9,1)$ is $d_{AB}=\sqrt{(9 + 9)^2+(1 - 6)^2}=\sqrt{18^2+( - 5)^2}=\sqrt{324 + 25}=\sqrt{349}$.
The distance between $B(9,1)$ and $C(9,6)$ is $d_{BC}=\sqrt{(9 - 9)^2+(6 - 1)^2}=\sqrt{0^2+5^2}=5$.
The distance between $A(-9,6)$ and $C(9,6)$ is $d_{AC}=\sqrt{(9 + 9)^2+(6 - 6)^2}=\sqrt{18^2+0^2}=18$.

Step2: Check for right - triangle using Pythagorean theorem

The Pythagorean theorem states that for a right - triangle $a^2 + b^2=c^2$, where $c$ is the longest side. Here, $d_{AB}^2 = 349$, $d_{BC}^2=25$, $d_{AC}^2 = 324$. Since $d_{BC}^2 + d_{AC}^2=25 + 324=349=d_{AB}^2$, the triangle is a right - triangle.

Answer:

Right Triangle