Question

question 1 - 7
the mid - point of $overline{lk}$ is $m(3,6)$. the coordinates for the point $l$ are $l(0,2)$. find the coordinates of the other endpoint $k$.

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 $L(x_1,y_1)=(0,2)$ and $K(x_2,y_2)$. The mid - point $M(3,6)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=3$. Substitute $x_1 = 0$ into the equation: $\frac{0 + x_2}{2}=3$, which simplifies to $\frac{x_2}{2}=3$. Multiply both sides by 2 to get $x_2=6$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=6$. Substitute $y_1 = 2$ into the equation: $\frac{2 + y_2}{2}=6$. Multiply both sides by 2: $2 + y_2=12$. Subtract 2 from both sides to get $y_2 = 10$.

Answer:

$(6,10)$