Question

graph △uvw with vertices u(3, 10), v(3, -7), and w(-6, 10). what is the area of △uvw? area = square units

Explanation:

Step1: Identify base and height

The points $U(3,10)$ and $V(3, - 7)$ have the same $x$ - coordinate. The distance between them is the height of the triangle. The points $U(3,10)$ and $W(-6,10)$ have the same $y$ - coordinate. The distance between them is the base of the triangle.
The height $h$ between $U(3,10)$ and $V(3,-7)$ is calculated as $h=\vert10-(-7)\vert=\vert10 + 7\vert=17$.
The base $b$ between $U(3,10)$ and $W(-6,10)$ is calculated as $b=\vert3-(-6)\vert=\vert3 + 6\vert=9$.

Step2: Apply triangle - area formula

The area formula for a triangle is $A=\frac{1}{2}bh$.
Substitute $b = 9$ and $h = 17$ into the formula: $A=\frac{1}{2}\times9\times17=\frac{153}{2}=76.5$.

Answer:

$76.5$