Question

What are the coordinates of the point on the directed line segment from

(-4,-9) to (1, 1) that partitions the segment into a ratio of 3 to 2?

Answer 1

(-1 , -3)

Step-by-step explanation

For unknown reason, I can't save the explanation in this space. It's detailed in the attachment

Answer 2

(- 1, - 3 )

Explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) partitioned in the ratio m : n

Then using the Section formula the coordinates of the point are

(
`(nx_(1)+mx_(2) )/(m+n)`,
`(ny_(1)+my_(2) )/(m+n)` )

Here (x₁, y₁ ) = (- 4, - 9), (x₂, y₂ ) = (1, 1) and m : n = 3 : 2 , then

(
`(2(-4)+3(1))/(3+2)` ,
`(2(-9)+3(1))/(3+2)` )

= (
`(x)/(y) (-8+3)/(5)`,
`(-18+3)/(5)` )

= (
`(-5)/(5)`,
`(-15)/(5)` )

= ( - 1, - 3 )