Question

The directed line segment from L to N has endpoints L(–6, 2) and N(5, –3). What are the x- and y-coordinates of point M, which partitions the directed line segment into the ratio 2:5?

x =

y =

Answer 1

x = \frac{ - 20}{7}

y=\frac{ 4}{7}

Explanation:

Answer 2

`x = ( - 20)/(7)`

`y=( 4)/(7)`

EXPLANATION

The x and y coordinates of the point that partition

`(x_1,y_1)`

and

`(x_2,y_2)`

in the ratio m:n is given by:

`x = (mx_(2) + nx_(1))/(m + n)`

and

`y= (my_(2) + ny_(1))/(m + n)`

The directed line segment from L to N has endpoints L(–6, 2) and N(5, –3).

We substitute the given points,

`x_1=-6`

`y_1=2`

`x_2=5`

`y_2=-3`

`m = 2`

`n = 5`

This implies that;

`x = (2(5)+ 5( - 6))/(2 + 5)`

`x = (10 - 30)/(2 + 5)`

`x = ( - 20)/(7)`

`y = (2( - 3)+ 5( 2))/(2 + 5)`

`y = ( - 6+ 10)/(2 + 5)`

`y=( 4)/(7)`