Question

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

Answer 1

Step-by-step explanation:

Given:-

points (-3, 10) and (6, 8)

To find:-

Find the ratio in which the line segment joining

points (-3, 10) and (6, 8) is divided by (-1,6).?

Solution:-

Given points are :(-3, 10) and (6, 8)

Let (x1, y1)=(-3,10)=>x1=-3 and y1=10

Let(x2, y2)=(6,8)=>x2=6 and y2=8

Given point = (-1,6)

Let the ratio be m1:m2

We know that

The coordinates of a point P (x,y) which divides the linesegment joining the points A (x1, y1) and

B(x2, y2) in the ratio m1:m2 internally is

[(m1x2+ m2x1)/(m1+m2),(m1y2+m2y1)/(m1+m2)]

[(m1(6)+m2(-3))/(m1+m2), (m1(8)+m2(10))/(m1+m2)]

[(6m1-3m2)/(m1+m2),(8m1+10m2)/(m1+m2)]=(-1,6)

On Comparing both sides then

(6m1-3m2)/(m1+m2)=-1

=> (6m1-3m2) = -1(m1+m2)

=> 6m1-3m2=-m1-m2

=>6m1+m1=-m2+3m2

=> 7m1=2m2

=>m1/m2=2/7

=>m1:m2=2:7

The ratio = 2:7

Answer:-

The required ratio for the given problem is 2:7

Used formulae:-

The coordinates of a point P (x,y) which divides the linesegment joining the points A (x1, y1) and

B(x2, y2) in the ratio m1:m2 internally is

[(m1x2+ m2x1)/(m1+m2),(m1y2+m2y1)/(m1+m2)]