Question

$overline{jk}$ has a mid - point at $m(4,1.5)$. point $j$ is at $(16, - 2)$. find the coordinates of point $k$. write the coordinates as decimals or integers. $k=(square,square)$

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 $J(x_1,y_1)=(16,-2)$ and $K(x_2,y_2)$. The mid - point $M(4,1.5)$.

Step2: Solve for $x$ - coordinate of $K$

We know that $\frac{x_1 + x_2}{2}=4$. Substitute $x_1 = 16$ into the equation: $\frac{16+x_2}{2}=4$. Multiply both sides by 2: $16 + x_2=8$. Then subtract 16 from both sides: $x_2=8 - 16=-8$.

Step3: Solve for $y$ - coordinate of $K$

We know that $\frac{y_1 + y_2}{2}=1.5$. Substitute $y_1=-2$ into the equation: $\frac{-2 + y_2}{2}=1.5$. Multiply both sides by 2: $-2+y_2 = 3$. Then add 2 to both sides: $y_2=3 + 2=5$.

Answer:

$(-8,5)$