Question

A, B, and C are collinear, and B is between A and C. The ratio of AB to BC is 1:2. If A is at (-9,-7) and B is at (-4,-6), what are the coordinates of point C

HELP THIS IS URGENT

Answer 1

use section formula point A and B is given and m=1 n=2 we get point c (6,-4)

Answer 2

Given :

A , B & C are collinear

AB:BC = 1:2

Coordinates of A is (-9,-7) & coordinates of B is (-4,-6).

To find : Coordinates Of point C

Solution :

•It is given that AB : BC = 1:2 & A , B, C are collinear , this means B divides AC in 1:2

•Let coordinates of C be (X,Y)

•By, Section formula

If A point divides a line in ratio of m1:m2 then coordinates of that point is given by ,

•x = (m2x1 + m1x2)/(m1+m2)

&

•y = (m2y1 + m1y2)/(m1+m2)

•Here , B divides Ac in 1:2

=> -4 =[ (2)(-9) + (1)(X)][1+2]

=> -4 = (-18 + X )/3

=> -12 = -18 + X

=> X = 6

•Also, -6 =[ (2)(-7) + (1)(Y)][1+2]

=> -6 = (-14 + Y )/3

=> -18 = -14 + Y

=> Y = -4

•Hence , coordinates of Point C are

( 6,-4)