Question

the mid - point n of (overline{jk}) has coordinates (4, 8). point j has coordinates (1, 6). find the coordinates of point k. write the coordinates as decimals or integers.

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the coordinates of point $J=(x_1,y_1)=(1,6)$ and the coordinates of point $K=(x_2,y_2)$ and the mid - point $M=(4,8)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=4$. Substitute $x_1 = 1$ into the equation: $\frac{1+x_2}{2}=4$. Multiply both sides by 2: $1 + x_2=8$. Then subtract 1 from both sides: $x_2=7$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=8$. Substitute $y_1 = 6$ into the equation: $\frac{6 + y_2}{2}=8$. Multiply both sides by 2: $6+y_2 = 16$. Then subtract 6 from both sides: $y_2 = 10$.

Answer:

$(7,10)$