Question

Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1,6)

Answer 1

the ratio in which the line is divided is 2:7

Let us consider a point P(-1, 6)(refer fig) that divides A(-3, 10) and B(6,-8) as per k:1 ratio, then we co-ordinates of P as (

k+1

6k−3

,

k+1

−8k+10

).

But we already have given co-ordinates of P,

∴

k+1

6k−3

=−1 and rewriting we have

6k−3=−k−1 or 6k+k=3−1 ∴7k=2 or k=

7

2

Thus, we get the point P dividing AB in the ratio 2:7.