Question

Point A has coordinates (7,2). Point B has coordinates (2,-10). Find the coordinates of point P that partition AB in the ratio of 5:1

Answer 1

`((17)/(6),-8)`.

Explanation:

We have been given that point A has coordinates (7,2). Point B has coordinates (2,-10). We are asked to find the coordinates of point P that partition AB in the ratio of 5:1.

We will use segment formula to solve our given problem.

When a point M divides a segment internally in ratio m:n, the coordinates of point M are:

`[x=(mx_2+nx_1)/(m+n),y=(my_2+ny_1)/(m+n)]`

`[x=(5*2+1*7)/(5+1),y=(5*(-10)+1*2)/(5+1)]`

`[x=(10+7)/(6),y=(-50+2)/(6)]`

`[x=(17)/(6),y=(-48)/(6)]`

`[x=(17)/(6),y=-8]`

Therefore, the coordinates of point P would be
`((17)/(6),-8)`.