Question

fg has a mid - point at m(20, 15.5). point g is at (20, 19). find the coordinates of point f. 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 the coordinates of point $F$ be $(x,y)$ and the coordinates of point $G$ be $(x_2,y_2)=(20,19)$ and the coordinates of mid - point $M$ be $(20,15.5)$.

Step2: Find the $x$ - coordinate of $F$

For the $x$ - coordinate, we have $\frac{x + x_2}{2}=x_M$. Substituting $x_2 = 20$ and $x_M=20$, we get $\frac{x + 20}{2}=20$. Multiply both sides by 2: $x + 20=40$. Then subtract 20 from both sides: $x=20$.

Step3: Find the $y$ - coordinate of $F$

For the $y$ - coordinate, we have $\frac{y + y_2}{2}=y_M$. Substituting $y_2 = 19$ and $y_M = 15.5$, we get $\frac{y+19}{2}=15.5$. Multiply both sides by 2: $y + 19 = 31$. Then subtract 19 from both sides: $y=12$.

Answer:

$(20,12)$