Question

the midpoint of $overline{gh}$ is $m(4.6, 11)$. one endpoint is $g(8.1, 6.7)$. 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 $G(x_1,y_1)=(8.1,6.7)$ and $H(x_2,y_2)$, and $M(4.6,11)$.

Step2: Solve for the x - coordinate of H

We know that $\frac{x_1 + x_2}{2}=4.6$ and $x_1 = 8.1$. Substitute $x_1$ into the formula: $\frac{8.1+x_2}{2}=4.6$. Multiply both sides by 2: $8.1 + x_2=9.2$. Then subtract 8.1 from both sides: $x_2=9.2 - 8.1=1.1$.

Step3: Solve for the y - coordinate of H

We know that $\frac{y_1 + y_2}{2}=11$ and $y_1 = 6.7$. Substitute $y_1$ into the formula: $\frac{6.7+y_2}{2}=11$. Multiply both sides by 2: $6.7 + y_2=22$. Then subtract 6.7 from both sides: $y_2=22 - 6.7 = 15.3$.

Answer:

$(1.1,15.3)$