Question

If the point $P(4,2)$ undergoes the following transformations successively.
$i)$ Reflection about the line $y=x,$
$ii)$ Translation through a distance of $5$ units along the positive $x-$ axis,
$iii)$ Reflection about $y=0$.
Then the coordinates of final position of $P$ are

• A. $(7,4)$
• B. $(7,-4)$
• C. $(7,3)$
• D. $(9,-4)$

Answer 1

The correct option is B $(7,-4)$

Given, $P\equiv (4,2)$
$i)$ After Reflection about $y-$axis, transformed coordinates will be $Q\equiv (2,4)$
$ii)$ After translation of $5$ units along positive $x-$ axis ,transformed coordinates will be $R(2+5,4)=R(7,4)$
$iii)$ Now, after reflection about $y=0$, coordinates of final position of $P\equiv (7,-4)$