Find the area of triangle NPQ.

Question

Points of Triangle NPQ

N (-14, -1) 

P (10, -3)

Q (6, 7)

Round only the final answer to 3 significant digits. Be sure to write the appropriate fornula and show your substitution.

Answer 1

Using the previous answer and showing NPQ is a right triangle, we can simply use the area formula - A = 1/2 bh.

Using the distance formula, d = √(x₂-x₁)² + (y₂-y₁)²

NQ = √(6+14)² + (7+1)²   NQ = √20² + 8² = √464

QP = √(10-6)² + (-3-7)²    QP = √4²+ (-10)² = √116

A = 1/2 (NQ)(QP) = 1/2 (√464)(√116) = 1/2 √53,824

A = 1/2 (232) = 116