Question

The midpoint of ST is M=(2, -1) One endpoint is S=(-4, 5) Find the coordinates of the other endpoint T

Answer 1

The x-coordinate, xm, of the midpoint is calculated as follows:

`x_M=(x_1+x_2)/(2)`

where x1 and x2 are the x-coordinates of the endpoints.

In the point M(2, -1), xm = 2. In S(-4, 5), x1 = -4. Substituting this information and solving for x2 (point T), we get:

`\begin{gathered} 2=(-4+x_2)/(2) \\ 2\cdot2=-4+x_2 \\ 4+4=x_2_{} \\ 8=x_2 \end{gathered}`

The x-coordinate of point T is 8.

The y-coordinate, ym, of the midpoint is calculated as follows:

`y_M=(y_1+y_2)/(2)`

where y1 and y2 are the x-coordinates of the endpoints.

In the point M(2, -1), ym = -1. In S(-4, 5), y1 = 5. Substituting this information and solving for y2 (point T), we get:

`\begin{gathered} -1=(5+y_2)/(2) \\ (-1)\cdot2=5+y_2 \\ -2-5=y_2 \\ -7=y_2 \end{gathered}`

The y-coordinate of point T is -7.

Point T has the coordinates (8, -7)