Question

What is the area, in square units, of ΔDEF with D(5,−1) E(1,−4), and F(−5,4)?

A. 25 square units
B. 37.5 square units
C. 50 square units
D. 75 square units

Answer 1

d got it correct on quiz

Answer 2

25

Explanation:

The line DF is

y+1 = -1/2 (x-5)

or

x+2y-3=0

The distance from E to that line is |1-8-3|/√(1^2+2^2) = 10/√5

The length of DF is √(10^2+5^2) = 5√5

So the area of DEF is 1/2 * 5√5 * 10/√5 = 25