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 (-21,-17), endpoint (-19,-15) the other endpoint is . (type an ordered pair.)

Explanation:

Step1: Recall mid - point formula

The mid - point formula between 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), $(x_2,y_2)=(-19,-15)$ and the mid - point $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})=(-21,-17)$.

Step2: Solve for x

We have $\frac{x+( - 19)}{2}=-21$. Multiply both sides by 2: $x - 19=-42$. Then add 19 to both sides: $x=-42 + 19=-23$.

Step3: Solve for y

We have $\frac{y+( - 15)}{2}=-17$. Multiply both sides by 2: $y - 15=-34$. Then add 15 to both sides: $y=-34 + 15=-19$.

Answer:

$(-23,-19)$