Question

the midpoint of $overline{jk}$ is $m(4, 9)$. one endpoint is $k(0, 10)$. find the coordinates of the other endpoint $j$. write the coordinates as decimals or integers. $j = ( , )$

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 $J=(x,y)$ and $K=(0,10)$ and $M=(4,9)$.

Step2: Solve for x - coordinate

We have $\frac{x + 0}{2}=4$. Cross - multiply: $x+0 = 8$, so $x = 8$.

Step3: Solve for y - coordinate

We have $\frac{y + 10}{2}=9$. Cross - multiply: $y + 10=18$. Subtract 10 from both sides: $y=18 - 10=8$.

Answer:

$(8,8)$