Question

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.

Answer 1

7x+2y = 4x + 5y
3x=3y
x = y
diagonal = 11x+7y-9=0
11x+7y = 9
18x = 9
x = 9/18
x = 1/2
y = 1/2
diagonal = 11/2+7/2 = 9
11+7/2
18/2
1st diagonal = 9 cm

2nd side = 7x + 2y + 0
7x+2y
7/2 + 2/2 = 0
7+2/2
9/2

opposite sides of a parallelogram are congruent.

1st side = 2nd side

Therefore, their diagonal s bisect each other and they are congruent.

1st diagonal = 2nd diagonal
2nd diagonal = 9 cm

Hope it helps.....

Answer 2

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) .

_______________

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 :

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