Question

question 13 of 16. the coordinates of the mid - point of gh are m(4,3) and the coordinates of one endpoint are g(5, - 6). 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 $G(x_1,y_1)=(5, - 6)$ and $H(x_2,y_2)$ be the endpoints and $M(4,3)$ be the mid - point.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1 = 5$ and $x_M=4$ into the formula: $\frac{5 + x_2}{2}=4$. Multiply both sides by 2: $5 + x_2=8$. Then subtract 5 from both sides: $x_2=8 - 5=3$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1=-6$ and $y_M = 3$ into the formula: $\frac{-6 + y_2}{2}=3$. Multiply both sides by 2: $-6 + y_2=6$. Then add 6 to both sides: $y_2=6 + 6 = 12$.

Answer:

$(3,12)$