(-5, 5) ; (x, 10) ; (10, 6) ; (-2, 1) are the co-ordinates of the vertices of a parallelogram. Find x.

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This question was previously asked in

ALP CBT 2 Physics and Maths Previous Paper 1 (Held On: 21 Jan 2019 Shift 1)

Answer 1

GIVEN:

Vertices of a parallelogram = (-5, 5) ; (x, 10) ; (10, 6) ; (-2, 1)

CONCEPT:

The diagonals of a parallelogram bisect each other.

FORMULAE USED:

Midpoint = \((\frac{x_1\ +\ x_2}{2},\ \frac{y_1\ +\ y_2}{2})\)

CALCULATION:

Here, O is the mid point of AC and BD becuase the diagonals of a parallelogram bisect each other.

Now, Mid of point of AC = Mid point of BD

⇒ \(\frac{-\ 5\ +\ 10}{2}\ =\ \ \frac{x\ +\ (-\ 2)}{2}\)

⇒ 5 = x - 2

⇒ x = 7

∴ The value of x is 7.

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