Question

If the points (-2,-1) (1,0) (x, 3) (3,y) form a parallelogram, find the values of x and y

Answer 1

The value of x is 6 and the value of y is 2.

Step-by-step explanation:

Consider A(-2, -1), B(1, 0), C(x, 3) and D(3, y) is a parallelogram,

∵ The diagonals of a parallelogram bisect each other.

The diagonals of ABCD are AC and BD,

So, Mid point of AC = mid point of BD

$(\frac{-2+x}{2}, \frac{-1+3}{2})=(\frac{1+3}{2}, \frac{0+y}{2})$

$(\frac{x-2}{2}, \frac{2}{2})=(\frac{4}{2}, \frac{y}{2})$

$(\frac{x-2}{2}, 1)=(2, \frac{y}{2})$

By comparing x-coordinates,

$\frac{x-2}{2}=2$

x-2 = 4

⇒ x = 4 + 2 = 6

And, comparing y-coordinates,

$1=\frac{y}{2}$

⇒ y = 2

Hence, the value of x is 6 and the value of y is 2.

#Learn more:

Properties of parallelogram :

https://brainly.in/question/728617

Answer 2

Step-by-step explanation:

A(-2,-1) B(1,0) C(x, 3) D(3,y)

Given that the points form parallelogram

Thus In llgm diagnols bisect each other

Mid point of AC = Midpoint of BD

(-2 + x)/2 , (-1+3) / 2 = (1 +3)/2 , (0+ y) / 2

( x - 2)/2, (2)/2 = (4/2) , y/2

(x-2)/2, 1 = 2, y/2

Taking common coordinates

(x-2)/2=2 1 = y/2

x-2=4 y = 2

x=6 y=2

Hope this answer is helpful