Question

what is the area of the triangle? (-4, -5) (1, -3) (1, -7) square units

Explanation:

Step1: Identify base and height

The base is the vertical distance between $(1, - 3)$ and $(1,-7)$. The height is the horizontal distance from $(1,-3)$ (or $(1, - 7)$) to $(-4,-5)$.
Base $b=\vert-3-(-7)\vert=\vert-3 + 7\vert = 4$.
Height $h=\vert1-(-4)\vert=\vert1 + 4\vert=5$.

Step2: Use area formula

The area formula for a triangle is $A=\frac{1}{2}bh$.
Substitute $b = 4$ and $h = 5$ into the formula: $A=\frac{1}{2}\times4\times5$.
$A = 10$.

Answer:

$10$