Dr. SK Goyal Solutions for Chapter: The Straight Lines, Exercise 5: INTRODUCTORY EXERCISE 2.5

The image of the point $\left(4,-3\right)$ with respect to the line $y=x$ is :

The co-ordinates of the foot of the perpendicular from $\left(2,3\right)$ to the line $3x+4y-6=0$ are :

The co-ordinates of the image of the origin $O$ with respect to the straight line $x+y+1=0$ are :

If $\left(-2,6\right)$ is the image of the point $\left(4,2\right)$ with respect to the line $L=0$, then $L\equiv$

The nearest point on the line $3x-4y=25$ from the origin is :

The image of the point $P(3, 8)$ in the line $x+ 3y - 7 = 0$ is

The image of a point $P\left(2,3\right)$ in the line mirror $y=x$ is the point $Q$ and the image of $Q$. in the line mirror $y=0$ is the point $R\left(x, y\right)$. Find the co-ordinates of $R$.

In a $∆ABC$, the equation of the perpendicular bisector of $AC$ is $3x-2y+8=0$. If the co-ordinates of the point $A$ and $B$ are $\left(1,-1\right)$ and $\left(3,1\right)$ respectively, find the equation of the line $BC$ and the centre of the circumcircle of $∆ABC$.