Question

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula,and solve the two equations for x and y.)midpoint (3,20), endpoint (10,13)The other endpoint is ___.(Type an ordered pair.)

Answer 1

The midpoint is (3,20) and the other endpoint is (10,13);

Since the midpoint formula is;

`(x_m,y_m)=((x_1+x_2)/(2),(y_1+y_2)/(2))`

Thus;

`\begin{gathered} x_m=(x_1+x_2)/(2) \\ 3=(x_1+10)/(2) \\ x_1+10=6 \\ x_1=-4 \end{gathered}`

and;

`\begin{gathered} y_m=(y_1+y_2)/(2) \\ 20=(y_1+13)/(2) \\ y_1+13=40 \\ y_1=27 \end{gathered}`

Thus, the other endpoint is;

`(-4,27)`