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

Answer:

$T = (20,25)$

Step-by-step explanation:

Given

$S = (-5,0)$

$M = (10,15)$

$Ratio = 3:2$

Required

Determine the coordinate of T

Line division by ratio is calculated using:

$M(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

Where:

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

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

$m:n = 3:2$

So, we have:

$(10,15) = (\frac{3 * x_2 + 2 * -5}{3+2},\frac{3 * y_2 + 2 * 0}{3+2})$

$(10,15) = (\frac{3x_2 -10}{5},\frac{3y_2}{5})$

Multiply through by 5

$5 * (10,15) = (\frac{3x_2 -10}{5},\frac{3y_2}{5}) * 5$

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

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

$T = (20,25)$