Question

the midpoint of $overline{gh}$ is $m(4.05, 0.45)$. one endpoint is $g(0.3, 10.6)$. find the coordinates of the other endpoint $h$. write the coordinates as decimals or integers. $h = (square,square)$

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 $G(x_1,y_1)=(0.3,10.6)$ and $H(x_2,y_2)$ and $M(4.05,0.45)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=4.05$. Substitute $x_1 = 0.3$ into the equation: $\frac{0.3+x_2}{2}=4.05$. Multiply both sides by 2: $0.3 + x_2=8.1$. Then subtract 0.3 from both sides: $x_2=8.1 - 0.3=7.8$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=0.45$. Substitute $y_1 = 10.6$ into the equation: $\frac{10.6 + y_2}{2}=0.45$. Multiply both sides by 2: $10.6+y_2 = 0.9$. Then subtract 10.6 from both sides: $y_2=0.9 - 10.6=-9.7$.

Answer:

$(7.8,-9.7)$