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 (-19,18), endpoint (-13,15)
The other endpoint is 1
(Type an ordered pair.)

Answer 1

The formula to calculate the midpoint between two points is given by

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

we have

M(-19,18)

(x1,y1)=(-13,15)

substitute given coordinates

$(-19,18)=(\frac{-13+x_2}{2},\frac{15+y_2}{2})$

step 1

Find out the value of the x2 -coordinate

we have the equation

$\begin{gathered} -19=\frac{-13+x_2}{2} \\ x_2-13=-38 \\ x_2=-38+13 \\ x_2=-25 \end{gathered}$

step 2

Find out the value of the y2-coordinate

we have the equation

$\begin{gathered} 18=\frac{15+y_2}{2} \\ \\ y_2+15=36 \\ y_2=36-15 \\ y_2=21 \end{gathered}$

therefore

The coordinates of the other endpoint are (-25,21)