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.
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Answer 1

Answer:

see the attachment for answer

Answer 2

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.