Question

If A(-2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram abcd, find the value of a and b. hence find the lengths of its sides.​

Answer 1

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Answer 2

Hey!
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➖❄Refer the Attachment for the figure❄➖
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Solution →Since the diagnols of a || gm bisect each other . Therefore the midpoint AC and BD coincide .

Mid Point => [( x1 + x2 / 2 ) , ( y1 + y2 /2) ]

◼For AC ,
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$= > ( \frac{ - 2 + 4}{2} ) \: ( \frac{b + 1}{2} )........eq.1$

◼For BD ,
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$= > (\frac{a + 1}{2 \: } ) \: \: ( \frac{0 + 2}{2} )........eq.2$

➖◾Equating the x and y coordinates from Eq. ( 1 ) and ( 2 )

$= > \frac{a + 1}{2} = 1 \\ = > a + 1 = 2$

•°• a = 1 ✔

Similarly ,

$= > \frac{b + 1}{2} = 1$

=> b = 1 ✔

➖❄Thus the values of a & b is equal to 1 .

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➖▪for finding the Length of its sides we need to calculate distance AB and AD .

Distance formula =

$= > \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} }$

❄For AB :
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$= > \sqrt{( 1+2) {}^{2} + (1 + 0) {}^{2} } \\ \\ = > \sqrt{10}$

❄For AD ,
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$= > \sqrt{ (- 2 - 1) {}^{2} + (1 - 2) {}^{2} }$

=> √10

▪➖We know that opposite sides of a || gm are equal . Here we have each of its side equal to √10

✔final answers :

➖)) a = 1 & b = 1

➖)) Length of each sides = √10

$Thanks!!$

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