Hello, wintersoltice!
3. A parallelogram $\displaystyle ABCD$ in which $\displaystyle A(8,2)$ and $\displaystyle B(2,6).$
The equation of $\displaystyle BC$ is: .$\displaystyle y\:=\:\frac{1}{2}x+5$
$\displaystyle X$ is the point on $\displaystyle BC$ such that $\displaystyle AX \perp BC$
Equation of $\displaystyle AX$ is: .$\displaystyle y\:=\:2x+18$ . . . . not needed
Coordinates of $\displaystyle X$ are $\displaystyle (5.2,7.6)$
Given that $\displaystyle BC = 5 BX$, find the coordinates of $\displaystyle C\text{ and }D.$ Code:

 o C
 *
 *
 X *
 * (5.2,7.6)
 B o *
 (2,6) *
 *
 *
 o(8,2)
 A
 +                 

$\displaystyle BC$ is five times $\displaystyle BX.$
Moving from B to X, we move 3.2 right and 1.6 up.
Moving from B to C, we will move 5 times as much.
. . $\displaystyle \begin{array}{ccccc}x &=& 2 + 5(3.2) &=& 18 \\ y &=& 6 + 5(1.6) &=& 14\end{array}\quad\Rightarrow\quad C(18,14)$
Moving from B to A, we move 6 right and 4 down.
Moving from C to D, we will move the same.
. . $\displaystyle \begin{array}{ccccc}x &=& 18 + 6 &=& 24 \\y &=& 14  4 &=& 10\end{array} \quad\Rightarrow\quad D(24,10)$