Question

Find point Z that partitions the directed line segment XY in the ratio of 5:3 where X(-2, 6) and Y(-10, -2).

Answer 1

`Z(x,y) = (-7 ,1)`

Explanation:

Given

`X(-2, 6); Y(-10, -2).`

`Ratio= 5:3`

Required

Point Z

Given that the line segment XY is divided into ratio;

The coordinates of point Z can be calculated using ratio formula given below

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

Where m and n are the ratio; m = 5 and n = 3

`(x_1, y_1) = (-2, 6); \\(x_2, y_2) = (-10, -2).`

So,

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

`Z(x,y) = ((5 * -10 + 3 * -2)/(5+3) ,(5 * -2 + 3 * 6)/(5+3))`

`Z(x,y) = ((-50 + -6)/(8) ,(-10 + 18)/(8))`

`Z(x,y) = ((-56)/(8) ,(8)/(8))`

`Z(x,y) = (-7 ,1)`

Hence, the coordinates of Z are (-7,1)