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

Answer:

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

Step-by-step 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

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

As given ratio is: 1:2

so m= 1

n = 2

Putting the values in the formula we get

$= (\frac{(2)(-6)+(1)(9)}{1+2} , \frac{(2)(-10)+(1)(2)}{1+2})\\=(\frac{-12+9}{3} , \frac{-20+2}{3})\\=(\frac{-3}{3} , \frac{-18}{3})\\=(-1,-6)$

Hence,

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