Question

graph △tuv with vertices t(0, 1), u(-7, -10), and v(-7, 1). what is the area of △tuv? area = square units

Explanation:

Step1: Identify base and height

The points $T(0,1)$ and $V(-7,1)$ have the same $y -$coordinate. The distance between them gives the base of the triangle. Using the distance formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ which is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, since $y_1 = y_2 = 1$, the base $b=\vert0-(-7)\vert=7$. The points $U(-7,- 10)$ and $V(-7,1)$ have the same $x -$coordinate. The distance between them gives the height of the triangle. Using the distance formula, since $x_1=x_2=-7$, the height $h=\vert1-(-10)\vert = 11$.

Step2: Apply area formula

The area formula for a triangle is $A=\frac{1}{2}bh$. Substitute $b = 7$ and $h = 11$ into the formula. So $A=\frac{1}{2}\times7\times11=\frac{77}{2}=38.5$.

Answer:

$38.5$