Question

suppose $overline{xy}$ has one endpoint at $x(0, 0)$. if $(3, 4)$ is the midpoint of $overline{xy}$, what are the coordinates of point $y?$

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $X(0,0)$ be $(x_1,y_1)$ and $Y(x,y)$ be $(x_2,y_2)$, and the mid - point be $(3,4)$.

Step2: Solve for $x$

We have $\frac{0 + x}{2}=3$. Multiply both sides by 2: $0 + x=6$, so $x = 6$.

Step3: Solve for $y$

We have $\frac{0 + y}{2}=4$. Multiply both sides by 2: $0 + y=8$, so $y = 8$.

Answer:

$(6,8)$