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 mid - point formula, and solve the two equations for x and y.) midpoint (-11,12), endpoint (-6,11)
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), $(x_2,y_2)=(-6,11)$ and the mid - point $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})=(-11,12)$.

Step2: Solve for x

We have $\frac{x+( - 6)}{2}=-11$. Multiply both sides by 2: $x - 6=-22$. Then add 6 to both sides: $x=-22 + 6=-16$.

Step3: Solve for y

We have $\frac{y + 11}{2}=12$. Multiply both sides by 2: $y+11 = 24$. Then subtract 11 from both sides: $y=24 - 11 = 13$.

Answer:

$(-16,13)$