Tag: reflection w.r.t a line

The new equation of the curve $4(x-2y+1)^{2}+9(2x+y+2)^{2}=25$ if the lines $2x+y+2=0$ and $x-2y+1=0$ are taken as the new $x$ and $y$ axes respectively is

The coordinates axes are rotated about the origin $O$ in the counter clockwise direction through an angle of $\dfrac{\pi}{6}$. If $a$ and $b$ are intercepts made on the new axes by a straight line whose equation referred to old the axes is $x+y=1$, then the value of $\displaystyle \frac{1}{a^{2}}+\displaystyle \frac{1}{b^{2}}$ is equal to

The reflection of the plane $x+y+z-3=0$ in the plane $2x+3y+4z-6=0$

Reflection of the line $\dfrac{x-1}{-1}=\dfrac{y-2}{3}=\dfrac{z-4}{1}$ in the plane $x+y+z=7$ is:

The image of the line $x-y-1=0$ in the line $2x-3y+1=0$ is

The image of the point A$(1,2)$ by the line mirror y=x and the image of B by the line mirror $y=0$ is the point $\left(\alpha, \beta \right)$, then :

A ray of light travelling along the line $x+\sqrt{3}y=5$ is incident on the $x-axis$ and after refraction it enters the other side of the $x-axis$ by turning $\dfrac{\pi}{6}$ away from the $x-axis$. The equation of the line along which the refracted ray travels is

If $B$ is reflection of $A(a,5)$ about line $4x-3y=0$, then area of triangle $ABC$ is equal to

Locus of the image of the point (2, 3) in the line (2x - 3y + 4) + k(x - 2y + 3) = 0, k $\in $ R, is a 

The distance of the image of a point (or an object) from the line of symmetry (mirror) is  ----- as that of the point (object )from the line (mirror).