Question

multiple choice 4 points
find the missing endpoint given that p(8, 7) is the midpoint of nq with n(2, 9)

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 $N(x_1,y_1)=(2,9)$ and $Q(x_2,y_2)=(x,y)$. Since $P(8,7)$ is the mid - point, we have $\frac{x_1 + x_2}{2}=8$ and $\frac{y_1 + y_2}{2}=7$.

Step2: Solve for $x$

We know that $\frac{2 + x}{2}=8$. Multiply both sides by 2: $2+x = 16$. Then subtract 2 from both sides: $x=16 - 2=14$.

Step3: Solve for $y$

We know that $\frac{9 + y}{2}=7$. Multiply both sides by 2: $9 + y=14$. Then subtract 9 from both sides: $y=14 - 9 = 5$.

Answer:

The missing endpoint $Q$ is $(14,5)$