Question

consider the following points. (-9,6), (9,1) and (9,6) step 2 of 2: what is the area of the triangle? (hint: make use of the mid - point formula if the triangle is isosceles.)

Explanation:

Step1: Recall the area formula for a triangle

The area formula for a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Identify the base and height

The two points $(9,1)$ and $(9,6)$ have the same $x -$coordinate. The distance between them is the height of the triangle. Using the distance formula for two points with the same $x -$coordinate $d = |y_2 - y_1|$, we have $h=|6 - 1|=5$.
The two points $(-9,6)$ and $(9,6)$ have the same $y -$coordinate. The distance between them is the base of the triangle. Using the distance formula for two points with the same $y -$coordinate $d=|x_2 - x_1|$, we have $b = |9-(-9)|=18$.

Step3: Calculate the area

Substitute $b = 18$ and $h = 5$ into the area formula $A=\frac{1}{2}bh$. So $A=\frac{1}{2}\times18\times5=45$.

Answer:

45