Question

On a coordinate plane, triangle DEF has points (-8, 8), (10, -2), and (-8, -8). Find the area of triangle DEF in square units.

Answer 1

The area of triangle DEF is 104 square units.

Step-by-step explanation:

To find the area of triangle DEF, we can use the Shoelace Formula. The formula states that if the vertices of a triangle are given by (x1, y1), (x2, y2), and (x3, y3), then the area of the triangle is given by:

A = 0.5 * |(x1*y2 + x2*y3 + x3*y1) - (x2*y1 + x3*y2 + x1*y3)|

Using the given coordinates (-8, 8), (10, -2), and (-8, -8), we can substitute the values into the formula to calculate the area of triangle DEF.

A = 0.5 * |(-8*(-2) + 10*(-8) + (-8)*8) - (10*8 + (-8)*(-8) + (-8)*(-2))|

Simplifying the expression gives us A = 0.5 * |(-16 - 80 - 64) - (80 + 64 - 16)| = 0.5 * |-160 - 48| = 0.5 * |-208| = 104 square units.