Question

If A(-2,-1), B(a,0), C(4, b) & D(1,2) are the vertices of a parallelogram, find the
values of a and b.
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Answer 1

Answer:

$\underline{\bigstar{\sf\ Given:-}}$

Vertices of a parallelogram =

A(-2,-1)

B(a,0)

C(5,b)

D(1,2)

$\underline{\bigstar{\sf\ To\:Find:-}}$

Values of a and b.

$\underline{\bigstar{\sf\ Solution:-}}$

Diaganols of parallelogram bisect each pther at O.

Mid point of AC = Mid point of BD

$\frac{x1 + x2}{2},\frac{y1 + y2}{2} = \frac{x1 + x2}{2},\frac{y1 + y2}{2} \\ \\ \frac{ - 2 + 4}{2} ,\: \frac{ - 1 + b}{2} = \frac{a + 1}{2} ,\: \frac{0 + 2}{2} \\ \frac{2}{2} ,\: \frac{ - 1 + b}{2} = \frac{a + 1}{2} , \: \frac{2}{2} \\ 1 ,\: \frac{ - 1 + b}{2} = \frac{a + 1}{2} , \: 1 \\ ⇒\frac{ - 1 + b}{2} = 1 \\ - 1 + b = 2 \\ b = 2 + 1 \\ ⇒b = 3 \\ \\ ⇒\frac{a + 1}{2} = 1 \\ a + 1 = 2 \\ a = 2 - 1 \\ ⇒a = 1$

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