Question

use the graph to find the coordinates of the missing endpoint if (p) is the mid - point of (overline{nq}).

1. (n(2,0),p(5,2))
2. (n(-5,4),p(-6,-3))

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $N(x_1,y_1)$ and $Q(x_2,y_2)$ with mid - point $P(x_m,y_m)$ is $x_m=\frac{x_1 + x_2}{2}$ and $y_m=\frac{y_1 + y_2}{2}$.

Step2: Solve for $x_2$ in the first problem

Given $N(2,0)$ and $P(5,2)$. For the $x$ - coordinate, $5=\frac{2 + x_2}{2}$. Cross - multiply: $10 = 2+x_2$. Then $x_2=10 - 2=8$.

Step3: Solve for $y_2$ in the first problem

For the $y$ - coordinate, $2=\frac{0 + y_2}{2}$. Cross - multiply: $4 = 0+y_2$. Then $y_2 = 4$. So the coordinates of $Q$ are $(8,4)$.

Step4: Solve for $x_2$ in the second problem

Given $N(-5,4)$ and $P(-6,-3)$. For the $x$ - coordinate, $-6=\frac{-5 + x_2}{2}$. Cross - multiply: $-12=-5 + x_2$. Then $x_2=-12 + 5=-7$.

Step5: Solve for $y_2$ in the second problem

For the $y$ - coordinate, $-3=\frac{4 + y_2}{2}$. Cross - multiply: $-6 = 4+y_2$. Then $y_2=-6 - 4=-10$. So the coordinates of $Q$ are $(-7,-10)$.

Answer:

1. $(8,4)$
2. $(-7,-10)$