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 (-18,4), endpoint (-11,5) the other endpoint is (type an ordered pair.)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $(x_1,y_1)=(x,y)$ (the unknown endpoint), $(x_2,y_2)=(-11,5)$ and the mid - point $(m_x,m_y)=(-18,4)$.

Step2: Solve for x - coordinate

We have $\frac{x+( - 11)}{2}=-18$. Multiply both sides by 2: $x - 11=-36$. Then add 11 to both sides: $x=-36 + 11=-25$.

Step3: Solve for y - coordinate

We have $\frac{y + 5}{2}=4$. Multiply both sides by 2: $y + 5=8$. Then subtract 5 from both sides: $y=8 - 5 = 3$.

Answer:

$(-25,3)$