Question

the midpoint of $overline{jk}$ is $m(-2.5, 0.05)$. one endpoint is $k(13.6, 12.2)$. find the coordinates of the other endpoint $j$. write the coordinates as decimals or integers. $j = ( square, square )$

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 $J=(x,y)$ and $K=(13.6,12.2)$ and $M=(-2.5,0.05)$.

Step2: Solve for x - coordinate of J

We know that $\frac{x + 13.6}{2}=-2.5$. Multiply both sides by 2: $x + 13.6=-5$. Then subtract 13.6 from both sides: $x=-5 - 13.6=-18.6$.

Step3: Solve for y - coordinate of J

We know that $\frac{y + 12.2}{2}=0.05$. Multiply both sides by 2: $y + 12.2 = 0.1$. Then subtract 12.2 from both sides: $y=0.1-12.2=-12.1$.

Answer:

$(-18.6,-12.1)$