Question

(iv) If A(1, 3); B( - 1, 2); C(x, 4) and. D(2, 5) are vertices of
parallelogram then write the value of x.​

Answer 1

Answer:

Given

A(1, 3); B( - 1, 2); C(x, 4) and. D(2, 5) are vertices of

parallelogram

To find

Value of x

Solution

If A,B,C and D are vertices of a parallelogram

implies Mid point of AC = Mid point of BD -----(1)

[because diagnols of a parallelogram bisect each other.]

Mid point of AC = (1+x/2, 3+4/2) -----(2)

Mid point of BD = (-1+2/2, 2+5/2) ------(3)

[Mid point is calculated using the formula

Mid point = (x1+x2/2, y1+y2/2)]

By Substituting value of (2) and (3) in (1) we get

(1+x/2,7/2) = (1/2,7/2)

By comparing both sides we get

1+x/2 = 1/2

1+x = 1 (After multiplying both sides by 2)

x = 1-1

x = 0

Therefore value of x is 0.

Hope it helps you.

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