Question

What are the coordinates of the point on the directed line segment from

(-6, -10) to (9, 2) that partitions the segment into a ratio of 1 to 2?

Answer 1

The coordinates of point that divides the given line in ratio 1:2 are (-1,-6)

Explanation:

Given that:

(x1,y1) = (-6,-10)

(x2,y2) = (9,2)

If a point (x,y) divides a line into ratio m:n, the coordinates can be found out by the formula

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

As given ratio is: 1:2

so m= 1

n = 2

Putting the values in the formula we get

`= (((2)(-6)+(1)(9))/(1+2) , ((2)(-10)+(1)(2))/(1+2))\\=((-12+9)/(3) , (-20+2)/(3))\\=((-3)/(3) , (-18)/(3))\\=(-1,-6)`

Hence,

The coordinates of point that divides the given line in ratio 1:2 are (-1,-6)