Question

practice: using midpoint formula question 16 of 16 16. the coordinates of the midpoint of $overline{gh}$ are $mleft(-\frac{13}{2},-6
ight)$ and the coordinates of one endpoint are $g(-4,1)$. find the coordinates of the other endpoint. the coordinates of the other endpoint are ( )( )

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $G(x_1,y_1)=(-4,1)$ and the mid - point $M(x_m,y_m)=(-\frac{13}{2},-6)$. Let the other endpoint be $H(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substitute $x_m =-\frac{13}{2}$ and $x_1=-4$ into the formula:
\[-\frac{13}{2}=\frac{-4 + x_2}{2}\]
Multiply both sides by 2: $-13=-4 + x_2$. Then add 4 to both sides: $x_2=-13 + 4=-9$.

Step3: Solve for $y_2$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substitute $y_m=-6$ and $y_1 = 1$ into the formula:
\[-6=\frac{1 + y_2}{2}\]
Multiply both sides by 2: $-12=1 + y_2$. Then subtract 1 from both sides: $y_2=-12 - 1=-13$.

Answer:

$(-9,-13)$