Find the area of the parallelogram whose sides are:
$x + 2 y + 3 = 0, 3 x + 4 y - 5 = 0, 2 x + 4 y + 5 = 0 a n d 3 x + 4 y - 10 = 0$

Open in App

Solution

Here $c_{1} = - \frac{3}{2}, c_{2} = - \frac{5}{4}, d_{1} = \frac{10}{4}, d_{2} = \frac{5}{4}, m_{1} = - \frac{1}{2}, m_{2} = - \frac{3}{4}$

$∴ A r e a = ∣ ∣ ∣ ∣ ∣ ∣ \frac{(- \frac{3}{2} + \frac{5}{4}) (\frac{10}{4} - \frac{5}{4})}{(- \frac{1}{2} + \frac{3}{4})} ∣ ∣ ∣ ∣ ∣ ∣ = \frac{5}{4}$ sq units

Suggest Corrections

Similar questions

If the area of the parallelogram whose sides are x + 2y + 3 = 0, 3x + 4y - 5 = 0, 2x+4y+5=0 and 3x + 4y - 10 = 0 is 'a' sq. unit. Find the value of 4a

___

Q. The four lines with equations

x + 2 y - 3 = 0, 3 x + 4 y - 7 = 0, 2 x + 3 y - 4 = 0, 4 x + 5 y - 6 = 0

Q. Find the position of the origin with respect to the triangle whose sides are

x + 1 = 0, 3 x - 4 y - 5 = 0, 5 x + 12 y - 27 = 0

Q. Find 'p'

3 x + 4 y - 5 = 0, 2 x + 3 y - 4 = 0, p x + 4 y - 6

are concurent.

Q. The equation of the tangents to the circle

x^{2} + y^{2} + 6 x + 6 y + 2 = 0

, which is parallel to

3 x + 4 y + 8 = 0

are

Join BYJU'S Learning Program

Find the area of the parallelogram whose sides are:x+2y+3=0,3x+4y−5=0,2x+4y+5=0 and 3x+4y−10=0

Here c1=−32,c2=−54,d1=104,d2=54,m1=−12,m2=−34 ∴Area=∣∣ ∣ ∣ ∣∣(−32+54)(104−54)(−12+34)∣∣ ∣ ∣ ∣∣=54 sq units

Find the area of the parallelogram whose sides are:
$x + 2 y + 3 = 0, 3 x + 4 y - 5 = 0, 2 x + 4 y + 5 = 0 a n d 3 x + 4 y - 10 = 0$