Question

A(2, 5), B(-1, 2) and C(5, 8) are the vertices of a triangle ABC, ‘M’ is a point on AB such that AM : MB = 1 : 2.

Answer 1

Given: A(2, 5), B(-1, 2) and C(5, 8) are the vertices of a triangle ABC, ‘M’ is a point on AB such that AM : MB = 1 : 2.

To find: Co-ordinates of 'M’ and the equation of the line passing through points C and M.

Solution:

• So as to find the coordinates of M, let the coordinates be (x,y).

• So we have the points as formula:

         mx2+nx1 / m+n and my2+ny1 / m+n

• So, coordinates are:

         1(-1) + 2(2) / 1+2 , 1(2) + 2(5) / 1+2

         -1 + 4 / 3 , 2 + 10 / 3

         M = (1 , 4)

• Now for the equation of line, slope of line passing through C and M is:

         m = 4-8 / 1-5 = 1

• So the slope obtained is 1.

• So the equation of line is:

         y - 8 = 1(x - 5)

         y - 8 = x - 5

        y = x + 3

Answer:

            So the coordinates of M is (1,4) and equation of line is y = x + 3.