Two consecutive sides of a parallelogram are 4x 5y 0

Asked by admin @ 04/08/2021 in Math viewed by 338 People

two consecutive sides of a parallelogram are 4x+5y=0 and 7x+2y+0 the equation of one diagonal is 11x+7y-9=0 find the equation of other diagonal.

Answered by admin @ 04/08/2021

AnswEr:

Let AB and AD be consecutive sides of parallelogram ABCD. Let the equations of AB and AB be 4x + 5y = 0 and 7x + 2y = 0 respectively. Clearly, these two lines intersect at A(0,0).

Solving 11x + 7y = 9 and 4x + 5y = 0, we get

x = 5/3
y = -4/3

So, the coordinates of B are (5/3, -4/3) .

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Similarly , by solving 11x + 7y = 9 and 7x + 2y = 0, we obtain that the coordinates of D are (-2/2, 7/3).

• We know that the diagonals of a llgm bisect each other. So, P is the mid point of BD and hence its coordinates are

$\hookrightarrow \sf \: [ \frac{ \frac{5}{3} - \frac{2}{3} }{2} , \frac{ \frac{ - 4}{3} + \frac{7}{3} }{2} ] \: \: \: or \: , \: ( \frac{1}{2} , \frac{1}{2} ) \\$

Clearly, AC passes through A(0,0) and C(1/2 , 1/2).

Hence, equation of AC is :

$\sf \: y - 0 = \frac{ \frac{1}{2} - 0}{ \frac{1}{2} - 0 } \: \: (x - 0), \: \: y = x$

Two consecutive sides of a parallelogram are 4x 5y 0

AnswEr:

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