Mathematics

Problem

Consider the triangle whose vertices are

P(m,1)

Q(4,3m)

and

R(2,-2)

. a. (i) Obtain a simplified expression in

m

for the area of the triangle

PQR

. Express your result without the absolute value sign. b. (ii) Hence find all real values of

m

for which the area of

PQR

is exactly

10

square units.