Question

the graph shows the vertices of a triangle. determine the area of the triangle. enter the unknown segment length(s), then calculate the area of the polygon. area of the triangle square units

Explanation:

Step1: Identify base and height

The base of the triangle is the distance between $L(-17,-3)$ and $Q(15,-3)$. The height is the vertical distance from $E(-1,5)$ to the line $y = - 3$.
The length of the base $b$:
The $x$-coordinates of $L$ and $Q$ are $x_1=-17$ and $x_2 = 15$. Using the distance formula for points on a horizontal line ($y$-coordinates are the same), $b=\vert x_2 - x_1\vert=\vert15-(-17)\vert=\vert15 + 17\vert=32$.
The height $h$:
The $y$-coordinate of $E$ is $y_1 = 5$ and the $y$-coordinate of the line containing the base is $y_2=-3$. So $h=\vert y_1 - y_2\vert=\vert5-(-3)\vert=\vert5 + 3\vert = 8$.

Step2: Apply triangle - area formula

The area formula of a triangle is $A=\frac{1}{2}bh$.
Substitute $b = 32$ and $h = 8$ into the formula: $A=\frac{1}{2}\times32\times8$.
$A = 16\times8=128$.

Answer:

128