Question

fg has a mid - point at m(12, 12.5). point f is at (10, 18). find the coordinates of point g. write the coordinates as decimals or integers.

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 $F=(x_1,y_1)=(10,18)$ and $G=(x_2,y_2)$. The mid - point $M=(12,12.5)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=12$. Substitute $x_1 = 10$ into the equation: $\frac{10+x_2}{2}=12$. Multiply both sides by 2: $10 + x_2=24$. Then subtract 10 from both sides: $x_2=24 - 10=14$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=12.5$. Substitute $y_1 = 18$ into the equation: $\frac{18+y_2}{2}=12.5$. Multiply both sides by 2: $18 + y_2=25$. Then subtract 18 from both sides: $y_2=25 - 18 = 7$.

Answer:

$(14,7)$