Question

Given the endpoint (-9,3) and (1,8) partition the segment into the ratio 2:3
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Answer 1

`P = (-5,5)`

Explanation:

Let the segments be A and B

`A = (-9,3)`

`B = (1,8)`

`m:n = 2:3`

Required

Determine the endpoints after it is divided into ratios.

Let the point be represented with P

The formula to use is:

`P = ((mx_2 + nx_1)/(m + n),(my_2 + ny_1)/(m + n))`

Where

`A = (-9,3)` -----
`(x_1,y_1)`

`B = (1,8)` ------
`(x_2,y_2)`

So:

`P = ((mx_2 + nx_1)/(m + n),(my_2 + ny_1)/(m + n))`

`P = ((2 * 1 + 3 * -9)/(2 + 3),(2 * 8 + 3 * 3)/(2 + 3))`

`P = ((-25)/(5),(25)/(5))`

`P = (-5,5)`