Mathematics

Problem

The vertices of a triangle are

A(2,3)

B(8,5)

and

C(4,9)

. a. (a) Find the mid-point

M

of the side

BC

. b. (b) Determine the coordinates of the centroid

G

of the triangle. c. (c) Show that the points

A

M

and

G

are collinear. d. (d) In what ratio does

G

divide the segment

AM

? Justify your answer.