To find the midpoint of a segment, we use the Midpoint Formula. However, how do you use this formula when the midpoint is known and we are looking for one of the endpoints?
Example Solution: (- k, - m) and (k,m).
Practice makes perfect
Let's draw an arbitrary segment through the origin where the coordinates of one endpoint is (k,m).
To find the midpoint of a segment, we use the Midpoint Formula:
M(x_1+x_2/2, y_1+y_2/2).
However, in this case we know the coordinates of the midpoint (0,0) and are looking for an endpoint. Therefore, the formula we have to use is
M_x = x_1+x_2/2 and M_y = y_1+y_2/2
By substituting the midpoint and our known coordinate, (k,m), we can solve for the second endpoint.
