Question

Point P divides the directed segment from A to B in the ratio 9 to 2. The coordinates of point A are

(-4,-2) and the coordinates of point P are (2, 1). Find the coordinates of point B. Round your answer to
the nearest tenth if necessary.

Answer 1

`B =(3.3,1.7)`

Explanation:

Given

`A(x_1,y_1) = (-4,-2)`

`P(x,y) = (2,1)`

`m : n = 9 : 2`

Required

The coordinates of
`B(x_2,y_2)`

The line segment from ratio is calculated as:

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

Substitute: A, P, m and n

`(2,1) = ((9 * x_2 + 2*-4)/(9+2),(9*y_2 +2 *-2)/(9+2))`

`(2,1) = ((9x_2 -8)/(11),(9y_2 -4)/(11))`

Multiply through by 11

`(22,11) = (9x_2 -8,9y_2 -4)`

By comparison:

`9x_2 - 8 = 22`

`9y_2 - 4 = 11`

So, we have:

`9x_2 - 8 = 22`

`9x_2 = 22 +8`

`9x_2 = 30`

Solve for x2

`x_2 = 30/9`

`x_2 = 3.3`

`9y_2 - 4 = 11`

`9y_2 = 11+4`

`9y_2 = 15`

Solve for y2

`y_2 =15/9`

`y_2 =1.7`

So, the coordinates of B is:

`B =(3.3,1.7)`