Mathematics

Problem

Points

P(1,4)

Q(5,8)

and

R(9,12)

are given in the plane. a. (a) Prove that the three points are collinear. b. (b) Write the equation of their common line in the intercept form

\dfrac{x}{a}+\dfrac{y}{b}=1

. c. (c) A point

S

divides the segment

PR

internally in the ratio

3:1

starting from

P

. Determine the coordinates of

S

and verify that it lies on the same line.