Question

Find the coordinates of the other endpoint of a segment with the given endpoint and Midpoint M.T(-8,-1)M(0,3)

Answer 1

If we have 2 endpoints (x1, y1) and (x2, y2), the coordinates of the midpoint will be:

`\begin{gathered} x=(x_1+x_2)/(2) \\ y=(y_1+y_2)/(2) \end{gathered}`

Now, we know the coordinates of one endpoint (x1, y1) equal to (-8, -1) and the midpoint (x, y) equal to (0,3), so we can replace those values and solve for x2 and y2.

Then, for the x-coordinate, we get:

`\begin{gathered} 0=(-8+x_2)/(2) \\ 0\cdot2=-8+x_2 \\ 0=-8+x_2 \\ 0+8=-8+x_2+8 \\ 8=x_2 \end{gathered}`

At the same way, for the y-coordinate, we get:

`\begin{gathered} 3=(-1+y_2)/(2) \\ 3\cdot2=-1+y_2 \\ 6=-1+y_2 \\ 6+1=-1+y_2+1 \\ 7=y_2 \end{gathered}`

Therefore, the coordinates of the other endpoint are (8, 7)

Answer: (8, 7)