How do you find the area of triangle DEF with the following coordinates: D(3,6), E(-2,-1), and F(-9,4)?

Answer 1

There are several ways to do this problem. The most straightforward is to realize that DE ⊥ FE (because the respective slopes are negative reciprocals). Draw a quick sketch to realize this might be the case before calculating the slopes. That means FE and DE are legs of a right triangle and can be treated as the base and height of the formula A = 1/2 BH.

Calculate the lengths of FE and DE and substitute into the above formula.

Try the above and check your answer here:

desmos.com/calculator/dbaca54eq5

Another way to do the problem would be to calculate the length of each side then use Heron's formula for the area of a triangle given the lengths of all three sides.