Question

If the points A(-2,-1), B(1,0),C(x,3) and D(1,y) are the vertices of a parallelogram , find the values of x and y. Without using distance formula.

Answer 1

the midpoint of diagnols is(1,1).
by using mid point formula-2+x/2=1
X=4 and y=2

Answer 2

Answer:

x = -2 and y = 4

Step-by-step explanation:

there is one important condition for parellogram i.e. two opp. sides are parallel to each other.

Hence, AB ║CD and  AC ║ BD

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

hence slope of AB = slope of CD

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

by this we get,

x + 3y = 10        ........(1)

now,

slope of AC = slope of BD

$\frac{-1-3}{-2-x}  = \frac{0-y}{1 - 1}$

here, if you see slope of BD is infinite.

thus, slope of AC is also infinite.

hence it is parallel to y-axis.Which means it has same x- co-ordinate.

therefore x co-ordinate of c = x co-ordinate of a

thus,  x = -2

substituting value of x in equation (1) we get value of y

y= 4.

THUS< ANSWER TO THIS PROBLEM IS X= -2 AND Y= 4.

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