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 ==> $\left( {\frac{3}{{\sqrt 2 }} - \frac{4}{{\sqrt 2 }},\frac{3}{{\sqrt 2 }} + \frac{4}{{\sqrt 2 }}} \right) = \left( {\frac{{ - 1}}{{\sqrt 2 }},\frac{7}{{\sqrt 2 }}} \right)$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from 9. straight line→9. straight line — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A circle of constant radius $' a '$ passes through origin $' O '$ and cuts the axes of co-ordinates in points $P$ and $Q$, then the equation of the locus of the foot of perpendicular from $O$ to $PQ $ is :

Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is

Equations to the circles which touch the lines $3x - 4y + 1 = 0$, $4x + 3y - 7 = 0$ and pass through $(2, 3)$ are

If equation of a line is 3x + 2y - 6 = 0 then x-intercept is and y-intercept is:

If ${x_n} = \frac{{2{n^2} + n + 1}}{{2{n^2} - 3n + 2}}$ ,then $\sum\limits_{r = 1}^n {\left[ {\left( {\prod\limits_{i = 1}^r {{x_i}} } \right) - 2\sum\limits_{i = 1}^r {\left( {2i - 1} \right)} } \right]} $ is equal to

Let $\frac{{1 - ix}}{{1 + ix}} = a - ib$ and ${a^2} + {b^2} = 1$, where $a$ and $b$ are real, then $x = $

The greatest integer less than or equal to ${(\sqrt 2 + 1)^6}$ is

Six boys and six girls sit along a line alternately in x ways and along a circle (again alternatively in y ways), then:

Choose the correct answer: The connective in the statement. “2 + 7 > 9 or 2 + 7 < 9” is

If $\frac{{z - \alpha }}{{z + \alpha }}\left( {\alpha \in R} \right)$ is a purely imaginary number and $\left| z \right| = 2$, then a value of $\alpha $ is