## Question

The area (in square units) of the quadrilateral formed by two pair of the lines

### Solution

We have,

Thus, the equations of the sides of the quadrilateral are

Clearly, they form of a parallelogram. Also, the distances between the pairs of parallel lines are same. So, they form a rhombus.

Area of parallelogram *OABC*

.

#### SIMILAR QUESTIONS

The straight lines represented by

The equation of the image of the pair of rays in the line mirror *x*= 1 is

Two lines represented by the equation are rotated about the point (1, 0), the line making the bigger angle with the positive direction of the *x*-axis being turned by 45^{o} in the clockwise sense and the other line being turned by 15^{o} in the anticlockwise sense. The combined equation of the pair of lines kin their new position is

The value of λ for which the lines joining the point of intersection of curves *C*_{1} and *C*_{2} to the origin are equally inclined to the axis of *X*.

If one of the lines given by the equation coincide with one of those given by and the other lines represented by them be perpendicular, then

If the pair of lines have exactly one line in common, then *a* =

If one of the given by , then *c*equals

Area of the triangle formed by the line *x* + *y* = 3 and angle bisectors of the pair of the straight lines is

If the The Pair of Straight Lines given by forms an equilateral triangle with the line *ax* + *by* + *c* = 0, then (*A* + 3*B*)(3*A* + *B*) =

The equation represets