Question

fg has a mid - point at m(4, 5). point g is at (2, 5). find the coordinates of point 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 the coordinates of point $F$ be $(x,y)$ and point $G(2,5)$ and mid - point $M(4,5)$.

Step2: Solve for the x - coordinate of point F

We know that $\frac{x + 2}{2}=4$. Multiply both sides by 2: $x + 2=8$. Then subtract 2 from both sides: $x=8 - 2=6$.

Step3: Solve for the y - coordinate of point F

We know that $\frac{y + 5}{2}=5$. Multiply both sides by 2: $y + 5=10$. Then subtract 5 from both sides: $y=10 - 5=5$.

Answer:

$(6,5)$