Question

A directed segment ST¯¯¯¯¯ is partitioned from S (−5,0) to T in a 32 ratio at point M (10, 15). What are the coordinates of point T? (20, 25) (15, 20) (7, 3) (5, 15

Answer 1

`T = (20,25)`

Explanation:

Given

`S = (-5,0)`

`M = (10,15)`

`Ratio = 3:2`

Required

Determine the coordinate of T

Line division by ratio is calculated using:

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

Where:

`(x_1,y_1) = (-5,0)`

`(x,y) = (10,15)`

`m:n = 3:2`

So, we have:

`(10,15) = ((3 * x_2 + 2 * -5)/(3+2),(3 * y_2 + 2 * 0)/(3+2))`

`(10,15) = ((3x_2 -10)/(5),(3y_2)/(5))`

Multiply through by 5

`5 * (10,15) = ((3x_2 -10)/(5),(3y_2)/(5)) * 5`

`(50,75) = (3x_2 -10,3y_2)`

By comparison:

`3x_2 - 10 = 50`

`3y_2 = 75`

`3x_2 - 10 = 50`

`3x_2 = 50 + 10`

`3x_2 = 60` --- Divide through by 3

`x_2 = 20`

`3y_2 = 75`

`y_2 =75/3` --- Divide through by 3

`y_2 =25`

Hence:

The coordinates of T is

`T = (20,25)`