Question

Find the coordinates of the other endpoint of the segment, given its midpoint and one endmidpoint (1,-1), endpoint (3,8)

Answer 1

Answer:

Explanation:

The midpoint (a, b) = (1, -1)

One endpoint, (x₁, y₁) = (3, 8)

The other endpoint, (x₂, y₂) = ?

Using the formula for midpoint and solving for the missing parameters

$\begin{gathered} a=\frac{x_1+x_2}{2} \\ \\ 1=\frac{3+x_2}{2} \\ \\ 2=3+x_2 \\ \\ x_2=2-3 \\ \\ x_2=-1 \end{gathered}$$\begin{gathered} b=\frac{y_1+y_2}{2} \\ \\ -1=\frac{8+y_2}{2} \\ \\ -2=8+y_2 \\ \\ y_2=-2-8 \\ \\ y_2=-10 \end{gathered}$

The coordinates of the other endpoint = (-1, -10)