Question

In the xy -coordinate plane, the coordinates of point s are (-2,-6), and coordinates of point T are (18,9). Point Q lies on line segment ST so that the ratio of the distance from point S to point Q to the distance from point g to point T is 2 to 3. What are the coordinates of point Q?

Answer 1

(6,0)

Explanation:

The coordinates of the points dividing the line segment in ratio m:n can be calculated as:

`((mx_(2)+nx_(1))/(m+n) ,(my_(2)+ny_(1))/(m+n) )`

Here x1, y1 are the coordinates of first point S (-2, -6) and x2, y2 are the coordinates of second point T(18, 9).

In this case m will be 2 and n will be 3 as the ratio is 2:3

Using all these values we can find the coordinates of point Q

`( (2(18)+3(-2))/(2+3),(2(9)+3(-6))/(2+3) )\\\\ = ((30)/(5) ,(0)/(5) )\\\\ =(6,0)`

Thus, the coordinates of point Q which divides the line segment ST in ratio of 2:3 are (6,0)