Analytic Geometry Question 2

In the standard $(x,y)$ coordinate plane, the point $(2,1)$ is the midpoint of $\overline{CD}$ . Point $C$ has coordinates $(6,8)$ . What are the coordinates of point $D$ ?

\displaystyle \left(-2,-\frac{7}{2}\right)

\displaystyle \left(-2,-6\right)

\displaystyle \left(4,\frac{9}{2}\right)

(10,10)

(10,15)

Approach

The midpoint has the average $x$ and $y$ values of the two points.

\dfrac{x_D+x_C}{2} = \overline{x}

\frac{x_D+6}{2} = 2

x_D+6 = 4

x_D = -2

\dfrac{y_D+y_C}{2} = \overline{y}

\frac{y_D+8}{2} = 1

y_D+8 = 2

y_D = -6