Question

find the coordinates of j if m(-5, 10) is the mid - point of segment jl, and l has coordinates of (6, 6).

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 the coordinates of $J$ be $(x,y)$ and the coordinates of $L$ be $(8,6)$ and the mid - point $M(-5,10)$.

Step2: Solve for $x$

We know that $\frac{x + 8}{2}=-5$. Cross - multiply: $x + 8=-10$. Then $x=-10 - 8=-18$.

Step3: Solve for $y$

We know that $\frac{y + 6}{2}=10$. Cross - multiply: $y + 6 = 20$. Then $y=20 - 6 = 14$.

Answer:

$(-18,14)$