Embibe Experts Solutions for Chapter: Point and Straight Line, Exercise 2: EXERCISE-2

The area enclosed by $2\left|x\right|+3\left|y\right|\le 6$ is-

The point $\left(4,1\right)$ undergoes the following three transformations successively-

(i) Reflection about the line $y=x$

(ii) Translation through a distance $2$ units along the positive directions of $x$-axis

(iii) Rotation through an angle $\frac{\pi }{4}$ about the origin.

The final position of the point is given by the coordinates:

Given the family of lines $a\left(3x+4y+6\right)+b\left(x+y+2\right)=0$. The line of the family situated at the greatest distance from the point $P\left(2,3\right)$ has equation-

Let $PQR$ be a right angled isosceles triangle, right angled at $P\left(2,1\right)$. If the equation of the line $QR$ is $2x+y=3$, then the equation representing the pair of lines  $PQ$ and $PR$ is-

Coordinates of a point which is at $3$ units distance from the point $\left(1,-3\right)$ on the line $2x+3y+7=0$ is/are-

The angle between the lines $y-x+5=0$ and $\sqrt{3}x-y+7=0$ is/are-

If line $y-x+2=0$is shifted parallel to itself towards the $x$-axis by a perpendicular distance of $3\sqrt{2}$ units, then the equation of the new line is may be-

The diagonals of a square are along the pair of lines whose equation is $2x^2-3xy-2y^2=0$. If $\left(2,1\right)$ is a vertex of the square, then the vertex of the square adjacent to it may be-