Question

1. reason suppose $overline{pq}$ has one endpoint at $p(0, 0)$. a. if $(2, 5)$ is the midpoint of $overline{pq}$, what are the coordinates of point $q$?

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $P(0,0)$ and $M(2,5)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1 = 0$ and $x_M=2$, we get $\frac{0 + x_2}{2}=2$. Cross - multiplying gives $0 + x_2=4$, so $x_2 = 4$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1 = 0$ and $y_M = 5$, we get $\frac{0 + y_2}{2}=5$. Cross - multiplying gives $0 + y_2=10$, so $y_2 = 10$.

Answer:

$(4,10)$