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