Question

find the coordinates of the missing endpoint if p is the midpoint of $overline{nq}$. n(5,4),p(6,3)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $P(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $N(x_1,y_1)=(5,4)$ and $P(x,y)=(6,3)$ and $Q(x_2,y_2)$.

Step2: Find the x - coordinate of Q

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

Step3: Find the y - coordinate of Q

We know that $y=\frac{y_1 + y_2}{2}$. Substituting $y = 3$ and $y_1 = 4$ into the formula:
$3=\frac{4 + y_2}{2}$
Multiply both sides by 2: $6=4 + y_2$.
Subtract 4 from both sides: $y_2=6 - 4=2$.

Answer:

$(7,2)$