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 $W(-6,10)$ 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 $d=\vert x_1 - x_2\vert$, we have $b=\vert3-(-6)\vert=\vert3 + 6\vert = 9$. The points $U(3,10)$ and $V(3,-7)$ 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 $d=\vert y_1 - y_2\vert$, we get $h=\vert10-(-7)\vert=\vert10 + 7\vert=17$.

Step2: Apply triangle - area formula

The area of a triangle is given by the formula $A=\frac{1}{2}bh$. Substituting $b = 9$ and $h = 17$ into the formula, we have $A=\frac{1}{2}\times9\times17=\frac{153}{2}=76.5$.

Answer:

$76.5$