Question

3. Line segment CD has endpoints at C( 7, -4) and D(-5, 4).

We want to find the coordinates of point P so that P partitions CD into a ratio of 3 to 1.

b. Fill in the correct values for the formula below:

P = ( + ( - ), + ( - )

Answer 1

P (- 2, 2 )

Explanation:

the section formula calculates a point P that partitions a line joining points

( x₁, y₁ ) and (x₂, y₂ ) in the ratio m : n , as

`x_(P)` =
`(mx_(2)+nx_(1) )/(m+n)` and
`y_(P)` =
`(my_(2)+ny_(1) )/(m+n)`

let (x₁, y₁ ) = C (7, - 4 ) and (x₂, y₂ ) = D (- 5, 4 ) , with m : n = 3 : 1

Then

`x_(P)` =
`(3(-5)+1(7))/(3+1)` =
`(-15+7)/(4)` =
`(-8)/(4)` = - 2

`y_(P)` =
`(3(4)+1(-4))/(3+1)` =
`(12-4)/(4)` =
`(8)/(4)` = 2

coordinates of point P (- 2, 2 )