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 (1,17), endpoint (-5,13)

Answer 1

The coordinates of a midpoint of a line delimited by two endpoints is:

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

Where (xm,ym) are the coordinates of the midpoint, (x1,y1) are the coordinates of the first endpoint and (x2,y2) are the coordinates of the second endpoint. We want to find (x2,y2), therefore:

`\begin{gathered} 1=(-5+x_2)/(2) \\ 2=-5+x_2 \\ x_2=2+5=7 \end{gathered}`
`\begin{gathered} 17=(13+y_2)/(2) \\ 34=13+y_2 \\ y_2=34-13 \\ y_2=21 \end{gathered}`

The coordinates of the endpoint two are (7,21).