Math, asked by elangovanpongaiyan, 9 months ago

If A(-2,-1) B(a,0) C(4,b) D(1,2) are the vertices of a parallelogram, Find the value of a & b.

Answers

Answered by shantiv87
8

Answer:

see the attachment for answer

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Answered by Anonymous
39

Question:

If A(-2,-1) B(a,0) C(4,b) D(1,2) are the vertices of a parallelogram, Find the value of a & b.

Answer:

✿Let a(-2,-1) , b(a,0) , c(4,b) and d(1,2) are the vertices of parallogram ABCD.

✷we know that diagonals of //gm intersect each other equally at o.

☆☆☆☆☆☆ AC=BD ☆☆☆☆☆☆

for finding AC

✷Therefore 0 divides AC and BD in the ratio 1:1

✿By Section formula....

,

point \: o = ( \frac{ m_{1} x_{1}   +  m_{2} x_{2}}{ \: m_{1}+m_{2}}  , \frac{m_{1} \:y_{2} +m_{2} \:y_{1} \: }{  m_{1}   + m_{2} } ) \\  \\   \implies( \frac{1(4) + 1( - 2)}{1 + 1} , \frac{1(b) + 1( - 1)}{1  + 1} ) \\  \\  \implies( \frac{4 - 2}{2}  -  \frac{b - 1}{2} ) \\  \\  \implies( \frac{2}{2} , \frac{b - 1}{2} ).......(1)</p><p></p><p></p><p>

Applying section formula on BD

point \: o = ( \frac{1(1) + 1(a)}{1 + 1} , \frac{1(2) + 1(0)}{1 + 1} )  \\  \\  \implies( \frac{1 + a}{2} , \frac{2 + 0}{2} ) \\  \\  \implies(  \frac{1 + a}{2} , \frac{1}{1} )...........(2)</p><p></p><p></p><p>

from (1) and (2),

( \frac{1}{1} ,\frac{b - 1}{2} ) = ( \frac{1 + a}{2} ,1)</p><p>

Taking,

 \frac{b - 1}{2}  = 1 \\  \\  \implies \: b - 1 = 2 \\  \\  \implies \: b = 3

 \frac{1 + a}{2}  = 1 \\  \\  \implies1 + a = 2 \\  \\ a = 1

Hence the coordinate of a and b are 1 and 3.

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BrainIyMSDhoni: Good
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