Question

Find the other end point of the line segment that has the given points: Endpoint: (5,1) Midpoint: (9,3)

Answer 1

The formula for the midpoint of a line segment:
$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
where x₁, y₁ - the coordinates of one endpoint; x₂, y₂ - the coordinates of the other endpoint

$\hbox{endpoint} - (5,1) \\ x_1=5 \\ y_1=1 \\ \\ \hbox{midpoint} - (9,3) \\ \Downarrow \\ \frac{5+x_2}{2}=9 \\ 5+x_2=18 \\ x_2=13 \\ \\ \frac{1+y_2}{2}=3 \\ 1+y_2=6 \\ y_2=5 \\ \\ \hbox{the other endpoint} - \boxed{(13,5)}$