Question

What is the area of a triangle whose vertices are D(3, 3) , E(3, −1) , and F(−2, −5) What is the area of the rectangle?

Answer 1

The area of the triangle with the given vertices is 10 square units

Explanation:

x y

D 3 3

E 3 -1

F -2 -5

D 3 3

Area: A=Abs [(xd ye + xe yf + xf yd) - (yd xe + ye xf + yf xd)] /2

Absolute value: Abs

A = Abs { [(3)(-1)+(3)(-5)+(-2)(3)] - [(3)(3)+(-1)(-2)+(-5)(3)] } / 2

A = Abs [ (-3-15-6)-(9+2-15) ] / 2

A = Abs [ (-24)-(-4) ] / 2

A = Abs ( -24+4) / 2

A = Abs (-20) / 2

A = 20 / 2

A = 10 square units