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 (24, - 17), endpoint (16, - 13)
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 $(x_1,y_1)=(16,-13)$ be the known endpoint and $(x_2,y_2)=(x,y)$ be the unknown endpoint, and the mid - point $(M_x,M_y)=(24,-17)$.

Step2: Solve for x

We know that $M_x=\frac{x_1 + x_2}{2}$. Substituting the values, we get $24=\frac{16 + x}{2}$. Multiply both sides by 2: $24\times2=16 + x$, so $48=16 + x$. Then subtract 16 from both sides: $x=48 - 16=32$.

Step3: Solve for y

We know that $M_y=\frac{y_1 + y_2}{2}$. Substituting the values, we get $-17=\frac{-13 + y}{2}$. Multiply both sides by 2: $-17\times2=-13 + y$, so $-34=-13 + y$. Then add 13 to both sides: $y=-34 + 13=-21$.

Answer:

$(32,-21)$