Question

If (-2,2),(1,0),(x,0),(1,y) form a parallelogram then (x,y) is
(A)(-4,-2)
(B)(4,-2)
(C)(-4,2)
(D)(4,2)​

Answer 1

Answer:

D. (4,2)

Step-by-step explanation:

A(-2,2),B (1,0), C(x,0), D(1,y)

slope of AB = CD

\begin{gathered}\frac{2 - 0}{ - 2 - 1} = \frac{0 - y} {x - 1}\\ 2x - 3y - 2 = 0\end{gathered}

−2−1

2−0

Answer 2

The values of (x,y) is (4,2)

Step-by-step explanation:

Given:

The vertices (-2,2),(1,0),(x,0),(1,y) form a parallelogram

To find:

(x,y)

Solution:

Let's name the parallelogram ABCD

The diagonals AC & BD will bisect each other

And hence, using the midpoint formula for AC & BD

A(-2,2), B(1,0), C(x,0), D(1,y)

$[\frac{-2+x}{2},\frac{2+0}{2}]= [\frac{1+1}{2},\frac{0+y}{2} ]$

$[\frac{x-2}{2},\frac{2}{2}]= [\frac{2}{2},\frac{y}{2} ]$

$[\frac{x-2}{2},1}]= [1},\frac{y}{2} ]$

Now we get, $\frac{x-2}{2}=1}\ \&\ \frac{y}{2} =1$

∴ $x-2=2\ \&\ y=2$

∴ $x= 2+2\ \& \ y=2$

∴ x= 4 & y=2

∴ (x,y)= (4,2)

#SPJ3