Question

A(2, 20), B(x,20), C (40,y), and D(10,6) are vertices of parallelogram taken in order, find x and y.

• A. $\begin{array}{c}x=32\\ y=32\end{array}$
• B. $\begin{array}{c}x=32\\ y=9\end{array}$
• C. $\begin{array}{c}x=44\\ y=8\end{array}$
• D. $\begin{array}{c}x=32\\ y=6\end{array}$

Answer 1

The correct option is D

$\begin{array}{c}x=32\\ y=6\end{array}$

The given points are

A(2,20),B(x,20), C(40, y), D(10,6)

Diagonals of a parallelogram bisect each other.

P(M,N)is the mid point of AC

P(M,N)is the mid point of BD

$(M,N)=(\frac{2+40}{2},\frac{y+20}{2})$

$(M,N)=(21,\frac{y+20}{2})-\left(1\right)$

$(M,N)=(\frac{x+10}{2},\frac{20+6}{2})$

$(M,N)=(\frac{x+10}{2},13)-\left(2\right)$

Form (1)and (2)

$\frac{x+10}{2}=21$

x =42-10

x=32

$\frac{y+20}{2}=13$

y =26-20

y =6