Question

fg has a mid - point at m(-10.75, -5.4). point g is at (-9.2, -9.3). 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 the coordinates of point $G$ be $(-9.2,-9.3)$ and the mid - point $M$ be $(-10.75,-5.4)$.

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

We know that $\frac{x+( - 9.2)}{2}=-10.75$. Multiply both sides by 2: $x - 9.2=-21.5$. Then add 9.2 to both sides: $x=-21.5 + 9.2=-12.3$.

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

We know that $\frac{y+( - 9.3)}{2}=-5.4$. Multiply both sides by 2: $y - 9.3=-10.8$. Then add 9.3 to both sides: $y=-10.8 + 9.3=-1.5$.

Answer:

$(-12.3,-1.5)$