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 (-11,12), endpoint (-5,3) 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 $(x_1,y_1)=(x,y)$ (unknown endpoint), $(x_2,y_2)=(-5,3)$ and the mid - point $(M_x,M_y)=(-11,12)$.

Step2: Set up equation for x - coordinate

We have $\frac{x+( - 5)}{2}=-11$. Multiply both sides by 2: $x - 5=-22$. Then add 5 to both sides: $x=-22 + 5=-17$.

Step3: Set up equation for y - coordinate

We have $\frac{y + 3}{2}=12$. Multiply both sides by 2: $y+3 = 24$. Then subtract 3 from both sides: $y=24 - 3=21$.

Answer:

$(-17,21)$