Question

what is the area of a triangle with vertices at $(-2,1),(2,1)$, and $(3,4)$? enter your answer in the box. units$^{2}$

Explanation:

Step1: Calculate the base length

The two points \((-2,1)\) and \((2,1)\) have the same \(y -\)coordinate. The distance between them (base \(b\)) is \(|2 - (-2)|=4\).

Step2: Calculate the height

The height \(h\) is the vertical distance from the line \(y = 1\) (where the base lies) to the point \((3,4)\). So \(h=|4 - 1| = 3\).

Step3: Use the triangle area formula

The area formula for a triangle is \(A=\frac{1}{2}\times b\times h\). Substitute \(b = 4\) and \(h=3\) into the formula: \(A=\frac{1}{2}\times4\times3\).
$$A=\frac{1}{2}\times4\times3=6$$

Answer:

\(6\)