Question

Calculate the ratio in which the line joining A(-4,2) and B(3,6) is divided by point p(x,3). Also, find x 

Answer 1

Let P (x,3) divides the line segment joining the points 

A(-4,2) and B(3,6) in the ratio K:1.

Thus , we have 

`(3k-4)/(k+1)=x;`    `(6k+2)/(k+1)=3`

for 

`6k+2=3(k+1)`

`⇒ 6k+2=3k+3`

`⇒3k=3-2`

`⇒3k=1⇒k=1/3`

∴ Required ratio` 1:3`

a now  consider the quation` (3k-4)/(k+1)=x`

Substituting the value of k in the above equation, We have 

` (3xx1/3-4)/(1/3+1)= x⇒ -3/(4/3)=x ⇒-9/4=x`

`∴ x=-9/4`

`b.AP=sqrt (((-9)/4+4)^2+(3-2)^2)=sqrt(49/16+1)=sqrt(49+16)/16=sqrt(65/16)`

`⇒ AP=sqrt 65/4 "unit"`