Math, asked by vyomrayal, 8 months ago

if A(-2,1) B(a,0) c (4,B) and d(1 ,2) is a pallogram find a and b​

Answers

Answered by udayteja5660
2

Answer:

a = 1 and b = 1

Step-by-step explanation:

A(-2,1) B(a,0) C(4,b) D(1,2) are vertices of parallelogram

AC and BD are diagonals

We know that

Midpoint of AC = Midpoint of BD

⇒ [ (4 + (-2))/2, (b + 1)/2 ] = [ (a + 1)/2, (0 + 2)/2 ] {∵mid point formula}

⇒ [ (4-2)/2, (b+1)/2 ] = [ (a + 1)/2, 2/2 ]

⇒ [ 1, (b+1)/2 ] = [ (a + 1)/2, 1 ]

Equating the respective coordinates( x and y coordinates) on both sides

⇒ 1 = (a + 1)/2  |    ⇒ (b+1)/2 = 1

⇒ a + 1 = 2      |    ⇒ b + 1 = 2

∴ a = 1             |      ∴ b = 1

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