First slide

Cartesian plane

Question

The point $(4, 1)$ undergoes the following
three transformations successively.
(i) reflection about the line $y = x$
(ii) transformation through a distance 2 units along the
positive direction of x- axis
$(iii)$ rotation through an angle p/4 about the origin in
the counter clockwise direction. Then the final position
of the point is given by the coordinates

Moderate

Solution

Reflection of the point (4, 1) about the line
$y = x$ is $(1, 4)$ which is transfered to the point $(3, 4)$ at a distance 2
units along the positive direction of x- axis
Finally a rotation through an angle $π / 4$ takes it to
$\begin{matrix} (3 \cos (π / 4) - 4 \sin (π / 4)), (3 \sin (π / 4) + 4 \cos (π / 4)) \\ = (\frac{- 1}{\sqrt{2}}, \frac{7}{\sqrt{2}}) \end{matrix}$

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