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 (15, - 10)
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 $(x_1,y_1)=(x,y)$ be the unknown endpoint, $(x_2,y_2)=(15,-10)$ and the mid - point $(m_x,m_y)=(21,-17)$.

Step2: Solve for x

We have $\frac{x + 15}{2}=21$. Multiply both sides by 2: $x + 15=42$. Then subtract 15 from both sides: $x=42−15 = 27$.

Step3: Solve for y

We have $\frac{y+( - 10)}{2}=-17$. Multiply both sides by 2: $y - 10=-34$. Then add 10 to both sides: $y=-34 + 10=-24$.

Answer:

$(27,-24)$