Tag: reflection w.r.t a line

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Questions Related to reflection w.r.t a line

Multiple choice maths does it look the same? reflection on coordinate axis reflection w.r.t a line reflection

A circle with centre $(1,1)$ intersects X axis at $(1,0)$ and  Y axis at $(0,1)$. Find the centre of the circle when reflected through X axis.

  1. $(1,-1)$
  2. $(1,1)$
  3. $(-1,-1)$

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
The graph is symmetric(reflection) w.r.t to the $x$-axis i.e. $y=0$ , If $(x,y)$ is a point on the graph ,then $(x,-y)$ is also a point on the graph .

Given center at $(1,1)$
using above concept reflection of center about $X$-axis lies at  $(1,-1)$
Multiple choice maths does it look the same? reflection on coordinate axis reflection w.r.t a line reflection

State whether true/false:
A shape is symmetrical if both sides of it are the same when a mirror line is drawn.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The line that divides a figure into identical halves is called the line of symmetry or the axis of symmetry. The line of symmetry is also called as mirror line because it produces two reflections of an image that coincide.

Multiple choice maths does it look the same? reflection on coordinate axis reflection w.r.t a line reflection

A circle with centre $(0,0)$ and of radius $2$ cm is plotted in the XY plane. Take the part of circle in first quadrant and find its reflection through X axis.

  1. The reflected image will form in $3rd$ quadrant.
  2. The reflected image will form in $1st$ quadrant.
  3. The reflected image will form in $2nd$ quadrant.
  4. The reflected image will form in $4rth$ quadrant.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
The graph is symmetric(reflection) w.r.t to the $x$-axis i.e. $y=0$ , If $(x,y)$ is a point on the graph ,then $(x,-y)$ is also a point on the graph .

in first quadrant both $x$ and $y$ are positive ,
using above concept ,all the point of circle which lie on the first quadrant has a reflection about $X$-axis at $(x,-y)$ .

And we know points $(x,-y)$ always lie in $4^{th}$ quadrant .
Multiple choice maths does it look the same? reflection on coordinate axis reflection w.r.t a line reflection

A circle with centre $(0,0)$ and of radius $2$ cm is plotted in the XY plane. Take the part of circle in first quadrant and find its reflection through Y axis.

  1. The reflected image would get formed in $1st$ quadrant.
  2. The reflected image would get formed in $2nd$ quadrant.
  3. The reflected image would get formed in $4rth$ quadrant.

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The graph is symmetric (reflection) w.r.t to the $y$-axis i.e. $x=0$ , If $(x,y)$ is a point on the graph ,then $(-x,y)$ is also a point on the graph .

As we know points $(x,y)$ lie at $1^{st}$ quadrant --------   (both $x$ and $y$ are positive ).
Using above concept , all the reflected points of first quadrant about $Y$-axis lie at $(-x,y)$.
And we know points $(-x,y)$ lie in $2^{nd}$ quadrant .

Multiple choice maths does it look the same? reflection on coordinate axis reflection w.r.t a line reflection

 Line symmetry and mirror reflection are naturally related to each other.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A figure may have both horizontal and vertical lines of reflection.An object and its images are always at the same distance from the surface of a mirror, which is called the mirror line. Line symmetry and mirror reflection are naturally related and linked to each other. So, the option is true.

Multiple choice maths does it look the same? reflection on coordinate axis reflection w.r.t a line reflection

The distance of the object from the mirror line is ____ the distance of the image from the mirror line.

  1. same as

  2. greater than

  3. less than

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

An objects and its image are always at the same distance from the surface of mirror,  which is called the mirror line. Therefore the distance of the object from the mirror line is same as the distance of the image from the mirror line

Multiple choice maths position and movement reflection w.r.t a line transformation transformation and symmetry in geometrical shapes

The line $3x-4y+7=0$ is rotated through an angle $\dfrac {\pi}{4}$ in clockwise direction about the point $\left (1,1\right)$. The equation of the line in its new position is

  1. $7y+x-6=0$
  2. $7y-x-6=0$
  3. $x+7y=8$
  4. $7y-x+6=0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given slope $=\dfrac{3}{4} < 1$
$< 45^{o}$
$\therefore $ after rational clock slope because negative
$\dfrac{m _1-m _{2}}{1+m _{1},m _{2}}=\tan 45$
$m _{1}=\dfrac{3}{4} \,\,\,m _{2}=$ new slope
$\left| \dfrac{\dfrac{3}{4}-m}{1+\dfrac{3}{4} m} \right|=1$
$\dfrac{3}{4}-m= \pm \left( 1+\dfrac{3}{4}m \right)$
$\dfrac{3}{4}-m=1+ \dfrac{3}{4} m$
$\dfrac{7}{4}m=\dfrac{-1}{4}$
$m=\dfrac{-1}{7}$ appeared 
$\therefore$ satisfy slope and pt in option to save time.
Multiple choice maths position and movement reflection w.r.t a line transformation transformation and symmetry in geometrical shapes

Let $\displaystyle A\equiv \left( 2,0 \right) $ and $\displaystyle B\equiv \left( 3,1 \right) $. The line $\displaystyle AB$ turns about $\displaystyle A$ through an angle $\displaystyle \frac { \pi  }{ 12 } $ in the clockwise sense, and the new position of $\displaystyle B$ is $\displaystyle B'$. Then $\displaystyle B'$ has the co-ordinates :-

  1. $\displaystyle \left( \frac { 2\sqrt { 2 } -\sqrt { 3 } }{ \sqrt { 2 } } ,\frac { 1 }{ \sqrt { 2 } } \right) $
  2. $\displaystyle \left( \frac { 2\sqrt { 2 } +\sqrt { 3 } }{ \sqrt { 2 } } ,\frac { 1 }{ \sqrt { 2 } } \right) $
  3. $\displaystyle \left( \frac { \sqrt { 3 } -2\sqrt { 2 } }{ \sqrt { 2 } } ,\frac { 1 }{ \sqrt { 2 } } \right) $
  4. $\displaystyle \left( \frac { \sqrt { 3 } -2\sqrt { 2 } }{ 2 } ,\frac { 1 }{ \sqrt { 2 } } \right) $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Slope of the line $\displaystyle AB=\frac { 0-1 }{ 2-3 } =1$
$\therefore \angle BAX={ 45 }^{ o }$
Given $\angle B'AB={ 15 }^{ o }\Rightarrow \angle B'AX={ 30 }^{ o }$
Therefore slope of the line $\displaystyle AB'=\tan { { 30 }^{ o } } =\frac { 1 }{ \sqrt { 3 }  } $
Now line $AB'$ makes an angle of ${ 30 }^{ o }$ with positive direction of $x$-axis and 
$AB'=AB=\sqrt { { \left( 3-2 \right)  }^{ 2 }+{ \left( 1-0 \right)  }^{ 2 } } =\sqrt { 2 } $
Therefore coordinates are $\displaystyle \left( 2+\sqrt { 2 } \cos { { 30 }^{ o } } ,0+\sqrt { 2 } \sin { { 30 }^{ o } }  \right) =\left( \frac { 2\sqrt { 2 } +\sqrt { 3 }  }{ \sqrt { 2 }  } ,\frac { 1 }{ \sqrt { 2 }  }  \right) $