Question

On segment TR, the midpoint is M(2,5) and the endpoint is R(6,1). Calculate the

coordinates of point T.

Answer 1

The coordinates of point T on segment TR, with midpoint M(2,5) and endpoint R(6,1), are T(-2,9). This is calculated by using the midpoint formula and solving for the unknown endpoint, T.

Step-by-step explanation:

To calculate the coordinates of point T on segment TR, we need to use the fact that M(2,5) is the midpoint between T and R(6,1). The midpoint of a segment is the average of the endpoints' coordinates.

Let's call the x-coordinate of T as xt and the y-coordinate as yt. Since M is the midpoint, its coordinates are the averages of the coordinates of T and R as follows:

• (xt + 6) / 2 = 2
• (yt + 1) / 2 = 5

By solving the equations:

• xt = 2 * 2 - 6 = -2
• yt = 2 * 5 - 1 = 9

This gives us the coordinates of point T as T(-2,9).