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 (9,5), endpoint (4,7) 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 $(x_1,y_1)=(4,7)$ and the mid - point $(M_x,M_y)=(9,5)$, and the unknown endpoint be $(x_2,y_2)=(x,y)$.

Step2: Solve for x

We know that $M_x=\frac{x_1 + x_2}{2}$, so $9=\frac{4 + x}{2}$. Multiply both sides by 2: $18 = 4+x$. Then subtract 4 from both sides: $x=18 - 4=14$.

Step3: Solve for y

We know that $M_y=\frac{y_1 + y_2}{2}$, so $5=\frac{7 + y}{2}$. Multiply both sides by 2: $10 = 7+y$. Then subtract 7 from both sides: $y=10 - 7 = 3$.

Answer:

$(14,3)$