Question

the midpoint of $overline{jk}$ is $m(6,0)$. one endpoint is $j(7,0)$. find the coordinates of the other endpoint $k$. 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 $J(x_1,y_1)=(7,0)$ and $K(x_2,y_2)$ and $M(x_m,y_m)=(6,0)$.

Step2: Find the x - coordinate of K

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting $x_m = 6$ and $x_1=7$ into the formula: $6=\frac{7 + x_2}{2}$. Multiply both sides by 2: $12=7 + x_2$. Then subtract 7 from both sides: $x_2=12 - 7=5$.

Step3: Find the y - coordinate of K

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting $y_m = 0$ and $y_1 = 0$ into the formula: $0=\frac{0 + y_2}{2}$. Multiply both sides by 2: $0=0 + y_2$. So $y_2 = 0$.

Answer:

$(5,0)$