If the reflection of a point $\mathrm{A}(2,3)$ in X -axis is B ; reflection of B in the line $x+y=0$ is C…
If the reflection of a point $\mathrm{A}(2,3)$ in X -axis is B ; reflection of B in the line $x+y=0$ is C and the reflection of C in $x-y=0$ is D then the point of intersection of the lines $\mathrm{CD}, \mathrm{AB}$ is
$(3,-2)$
$(0,1)$
$(4,-3)$
$(2,-1)$
Solution
We know, reflection about X -axis of $(x, y)$ is $(x,-y)$
So, co-ordinates of B are $(2,-3)$
We know, reflection about line $x+y=0$ of $(x, y)$ is $(-y,-x)$
So, co-ordinates of C are $(3,-2)$
We know, reflection about $x-y=0$ of $(x, y)$ is $(y, x)$
So, co-ordinates of $D$ are $(-2,3)$
Equation of AB is, $y-3=\frac{-3-3}{2-2}(x-2) \Rightarrow x=2$
Equation of CD is, $y+2=\frac{3+2}{-2-3}(x-3) \Rightarrow x+y=1$
$\therefore$ Point of intersection of line AB and CD is $(2,-1)$