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 (9,7), endpoint (1, - 2) 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 $(x_1,y_1)=(1,-2)$ and the mid - point $(a,b)=(9,7)$. We want to find $(x_2,y_2)=(x,y)$.

Step2: Solve for x

We know that $a=\frac{x_1 + x_2}{2}$, so $9=\frac{1 + x}{2}$. Cross - multiply: $18 = 1+x$. Then $x=18 - 1=17$.

Step3: Solve for y

We know that $b=\frac{y_1 + y_2}{2}$, so $7=\frac{-2 + y}{2}$. Cross - multiply: $14=-2 + y$. Then $y=14 + 2 = 16$.

Answer:

$(17,16)$