Question

the midpoint of $overline{jk}$ is $m(-5.55, 5.25)$. one endpoint is $j(-5.6, 2.7)$. find the coordinates of the other endpoint $k$. write the coordinates as decimals or integers. $k = ( , )$

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 $J(x_1,y_1)=(-5.6,2.7)$ and $K(x_2,y_2)$. The mid - point $M(-5.55,5.25)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-5.55$. Substitute $x_1=-5.6$ into the equation: $\frac{-5.6 + x_2}{2}=-5.55$. Multiply both sides by 2: $-5.6+x_2=-11.1$. Then $x_2=-11.1 + 5.6=-5.5$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=5.25$. Substitute $y_1 = 2.7$ into the equation: $\frac{2.7+y_2}{2}=5.25$. Multiply both sides by 2: $2.7+y_2 = 10.5$. Then $y_2=10.5 - 2.7 = 7.8$.

Answer:

$(-5.5,7.8)$