Question

in the standard (x,y) coordinate plane below, the points (-5,0), (5,0), and (0,6) are vertices of a triangle. what is the area, in square coordinate units, of the triangle? 18√2 30 24√2 30√3

Explanation:

Step1: Calculate the base length

The two points \((-5,0)\) and \((5,0)\) are on the \(x -\)axis. The distance between them (base \(b\)) is \(|5 - (-5)|=10\) units.

Step2: Determine the height

The point \((0,6)\) gives the height \(h\) of the triangle. The \(y -\)coordinate of this point is the height, so \(h = 6\) units.

Step3: Use the triangle area formula

The area formula for a triangle is \(A=\frac{1}{2}\times b\times h\). Substitute \(b = 10\) and \(h=6\) into the formula: \(A=\frac{1}{2}\times10\times6\).

Answer:

\(30\)