Question

the mid - point of fg is m(15, - 2.5). one endpoint is g(16, 6). find the coordinates of the other endpoint f. write the coordinates as decimals or integers. f=( , )

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 $F=(x_1,y_1)$ and $G=(x_2,y_2)=(16,6)$, and $M=(15,-2.5)$.

Step2: Solve for $x$ - coordinate of $F$

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_2 = 16$ and $x_M=15$ into the formula: $\frac{x_1+16}{2}=15$. Multiply both sides by 2: $x_1 + 16=30$. Then subtract 16 from both sides: $x_1=30 - 16=14$.

Step3: Solve for $y$ - coordinate of $F$

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_2 = 6$ and $y_M=-2.5$ into the formula: $\frac{y_1+6}{2}=-2.5$. Multiply both sides by 2: $y_1 + 6=-5$. Then subtract 6 from both sides: $y_1=-5 - 6=-11$.

Answer:

$(14,-11)$