Question

use the coordinate plane below to answer the question. a triangle has vertices at $(-2,-3),(4,-3)$, and $(3,5)$. what is the area of the triangle?

Explanation:

Step1: Find the base length

The two points \((-2,-3)\) and \((4,-3)\) have the same \(y -\)coordinate.
The distance between them (base \(b\)) is \(|4 - (-2)|=|4 + 2| = 6\)

Step2: Find the height

The height \(h\) is the vertical distance from the line \(y=-3\) (where the base lies) to the point \((3,5)\).
\(h=|5-(-3)|=|5 + 3|=8\)

Step3: Calculate the area of the triangle

The area formula for a triangle is \(A=\frac{1}{2}\times b\times h\)
Substitute \(b = 6\) and \(h = 8\) into the formula: \(A=\frac{1}{2}\times6\times8\)
\(A = 3\times8=24\)

Answer:

\(24\)