If given the midpoint and one endpoint of a line segment, what must you do to find the other endpoint?

When you have the midpoint of a line segment and one endpoint, the correct approach to find the other endpoint involves understanding how the midpoint is calculated. The midpoint is the average of the coordinates of the two endpoints.

To find the other endpoint, you would rearrange the midpoint formula. If you denote the known endpoint as ( E_1(x_1, y_1) ) and the midpoint as ( M(x_m, y_m) ), the midpoint formula is given by:

[

M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)

]

Here, ( (x_2, y_2) ) represents the coordinates of the other endpoint ( E_2 ) that we need to find. Instead of subtracting or averaging, you can rearrange the midpoint formula to solve for the other endpoint's coordinates:

[

x_m = \frac{x_1 + x_2}{2} \implies x_2 = 2x_m - x_1

]

[

y_m = \frac{y_1 + y_2}{2} \implies y_