Question

A line segment has endpoints S(-9, -4) and T(6, 5). Point R lies on segment ST such that the ratio of SR to RT is 2:1. What are the coordinates of point R?

Answer 1

To find the coordinates of point R on the line segment with endpoints S(-9, -4) and T(6, 5) such that SR to RT is 2:1, we find the distance between the endpoints and use the ratio to find the coordinates of R.

Step-by-step explanation:

To find the coordinates of point R, we first find the distance between the endpoints of the line segment:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance = √((6 - (-9))^2 + (5 - (-4))^2)

Distance = √(15^2 + 9^2)

Distance = √(225 + 81)

Distance = √306

Next, we can use the ratio of SR to RT to find the coordinates of R:

SR/RT = 2/1

Let SR = 2x and RT = x

We can set up two equations:

2x + x = √306

3x = √306

x = √306/3

Therefore, RT = √306/3 and SR = 2√306/3

Finally, we can find the coordinates of R:

Rx = Sx + SR = -9 + 2√306/3

Ry = Sy + SR = -4 + 2√306/3