The point (4, 1) undergoes the following three transformations su… - Vidyadip

MCQ

The point $(4, 1)$ undergoes the following three transformations successively (i) Reflection about the line $y = x$ (ii)Translation through a distance $2$ units along the positive direction of $x$ - axis (iii) Rotation through an angle $\pi /4$ about the origin in the anti clockwise direction. The final position of the point is given by the coordinates

A
$\left( {\frac{1}{{\sqrt 2 }},\frac{7}{{\sqrt 2 }}} \right)$
B
$( - \sqrt 2 ,\,\,7\sqrt 2 )$
✓
$\left( { - \frac{1}{{\sqrt 2 }},\frac{7}{{\sqrt 2 }}} \right)$
D
$(\sqrt 2 ,\,\,7\sqrt 2 )$

✓

Answer

Correct option: C.

$\left( { - \frac{1}{{\sqrt 2 }},\frac{7}{{\sqrt 2 }}} \right)$

c
(c) $({x_1},{y_1}) \to \left( {\frac{{{y_1} - 1}}{{{x_1} - 4}}} \right) = - 1$ and $\frac{{{x_1} + 4}}{2} = \frac{{{y_1} + 1}}{2}$
==> ${x_1} + {y_1} = 5$ and ${x_1} - {y_1} = - 3$==> ${x_1} = 1,{y_1} = 4$
${2^{nd}}$ operation ==> $(3,4)$
${3^{rd}}$ operation ==> $\left( {\frac{3}{{\sqrt 2 }} - \frac{4}{{\sqrt 2 }},\frac{3}{{\sqrt 2 }} + \frac{4}{{\sqrt 2 }}} \right) = \left( {\frac{{ - 1}}{{\sqrt 2 }},\frac{7}{{\sqrt 2 }}} \right)$.

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