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# If the Points (−2, −1), (1, 0), (X, 3) and (1, Y) Form a Parallelogram, Find the Values of X and Y. - CBSE Class 10 - Mathematics

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#### Question

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

#### Solution

Let ABCD be a parallelogram in which the coordinates of the vertices are A (−2,−1); B (1, 0); C (x, 3) and D (1, y).

Since ABCD is a parallelogram, the diagonals bisect each other. Therefore the mid-point of the diagonals of the parallelogram will coincide.

In general to find the mid-point P(x,y) of two points A(x_1, y_1) and B(x_2, y_2) we use section formula as,

P(x, y) = ((x_1+ x_2)/2, (y_1 + y_2)/2)

The mid-point of the diagonals of the parallelogram will coincide.

So,

Coordinate of the midpoint of AC = Coordinate of mid-point of BD

Therefore,

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

Now equate the individual terms to get the unknown value. So,

(x - 2)/2 = 1

x =4

Similarly,

(y + 0)/2= 1

y = 2

Therefore

x = 4 and y = 2

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Solution If the Points (−2, −1), (1, 0), (X, 3) and (1, Y) Form a Parallelogram, Find the Values of X and Y. Concept: Section Formula.
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