Question

the coordinates of the vertices of the triangle are (-8, 8), (-8, -4), and consider qr the base of the triangle. the measure of the base is b = 18 units, and the measure of the height is h = the area of triangle pqr is square units 54 108 112 144

Explanation:

Step1: Find the third - vertex

We know two vertices are $(-8,8)$ and $(-8, - 4)$. Since the base length is $b = 18$ units. Let the third vertex be $(x,y)$. The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. If one of the known points is $(-8,8)$ and the base length from a point on the vertical line $x=-8$ to the third - vertex is 18 units. Looking at the graph, the third vertex is $(10,-4)$.

Step2: Calculate the height

The height of a triangle with base along a horizontal or vertical line is the perpendicular distance from the opposite vertex to the base. The two points on the base are $(-8,-4)$ and $(10,-4)$. The opposite vertex is $(-8,8)$. The height $h$ is the vertical distance from $y = - 4$ to $y = 8$. So $h=\vert8-(-4)\vert=12$ units.

Step3: Calculate the area

The area of a triangle is given by the formula $A=\frac{1}{2}bh$. We know $b = 18$ units and $h = 12$ units. So $A=\frac{1}{2}\times18\times12=108$ square units.

Answer:

The coordinates of the third vertex are $(10,-4)$, the height $h = 12$ units, and the area of triangle $PQR$ is 108 square units.