Question

point h is the midpoint of $overline{fg}$. what is the value of y?
$g(4x, 6y + 6)$
$h(4, 15)$
$f(2y + 2, 2x + 4)$
$y = square$

Explanation:

Step1: Use mid - point formula for y - coordinate

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For the y - coordinates, we have $\frac{(6y + 6)+(2x + 4)}{2}=15$.

Step2: Simplify the equation

First, multiply both sides of the equation $\frac{6y+6 + 2x + 4}{2}=15$ by 2 to get $6y+2x+10 = 30$. Then, we can express it as $6y+2x=20$ or $3y + x=10$, so $x = 10 - 3y$.

Step3: Use mid - point formula for x - coordinate

For the x - coordinates, $\frac{4x+(2y + 2)}{2}=4$. Multiply both sides by 2: $4x+2y+2 = 8$, which simplifies to $4x+2y=6$ or $2x + y=3$.

Step4: Substitute x

Substitute $x = 10 - 3y$ into $2x + y=3$. We get $2(10 - 3y)+y=3$.

Step5: Expand and solve for y

Expand: $20-6y + y=3$. Combine like - terms: $20-5y=3$. Subtract 20 from both sides: $-5y=3 - 20=-17$. Divide both sides by $-5$: $y=\frac{17}{5}=3.4$.

Answer:

$3.4$