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 (-5, -12), endpoint (-1, -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 $(x_1,y_1)=(x,y)$ (the unknown endpoint), $(x_2,y_2)=(-1,-3)$ and the mid - point $(M_x,M_y)=(-5,-12)$.

Step2: Solve for x

We have $\frac{x+( - 1)}{2}=-5$. Multiply both sides by 2: $x - 1=-10$. Then add 1 to both sides: $x=-10 + 1=-9$.

Step3: Solve for y

We have $\frac{y+( - 3)}{2}=-12$. Multiply both sides by 2: $y-3=-24$. Then add 3 to both sides: $y=-24 + 3=-21$.

Answer:

$(-9,-21)$