Question

graph δabc with vertices a(1, -10), b(1, 8), and c(-3, -10). what is the area of δabc? area = square units

Explanation:

Step1: Identify base and height

The points $A(1,-10)$ and $C(-3,-10)$ have the same $y -$coordinate. The length of the base $b$ between $A$ and $C$ is found using the distance formula for two points on a horizontal line $d=\vert x_1 - x_2\vert$. Here, $b=\vert1-(-3)\vert=\vert1 + 3\vert = 4$. The points $A(1,-10)$ and $B(1,8)$ have the same $x -$coordinate. The height $h$ from $A$ to $B$ is found using the distance formula for two points on a vertical line $d=\vert y_1 - y_2\vert$. So, $h=\vert- 10 - 8\vert=\vert-18\vert = 18$.

Step2: Apply area formula

The area formula for a triangle is $A=\frac{1}{2}bh$. Substitute $b = 4$ and $h=18$ into the formula: $A=\frac{1}{2}\times4\times18$.

Step3: Calculate the area

$\frac{1}{2}\times4\times18=2\times18 = 36$.

Answer:

36