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Reflection on coordinate axis - class-X

Description: reflection on coordinate axis
Number of Questions: 18
Created by:
Tags: vectors and transformations maths does it look the same? transformation and symmetry in geometrical shapes reflection
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If P is (-3, 4) and My Mx (P)  shows the reflection of the  point P in the x"axis and then  the reflection of the image in the  y"axis, then My Mx (P) is

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

  1. (3, 4)

  2. (- 3, - 4)

  3. (`3, 4)

  4. (3, - 4)

Show answer
Correct Option: D

When an object is reflected in the mirror, the corresponding lengths and angles of the object and the image

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

  1. remain same

  2. increase in the image

  3. decrease in the image

  4. cannot be determined

Show answer
Correct Option: A
Explanation:

When an object is reflected, there is no change in the lengths and angles; i.e. the lengths and angles of the object and the corresponding lengths and angles of the image are the same. However, in one aspect there is a change, i.e. there is a difference between the object and the image. The left and the right sides of an object appear inverted in a mirror
hence option A is correct

If a boy, standing in front of a mirror has his right hand in the pocket, then in his mirror reflection, it will appear as

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

  1. his left hand in the pocket

  2. missing hand

  3. his right hand in the pocket

  4. can't say

Show answer
Correct Option: A
Explanation:

A plane mirror has a property of lateral inversion, which states that reflection of an object in the mirror will always be laterally inverted.

$\Rightarrow$ Right hand in the pocket will appear as left hand in the pocket.

Let R be the relation on the set R of all real numbers defined by a R b if $|a-b|\leq \dfrac{1}{2}$. Then R is?

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

  1. Reflexive and symmetric but not transitive

  2. Symmetric and transitive but not reflexive

  3. Transitive but neither reflexive nor symmetric

  4. Reflexive, symmetric and transitive

Show answer
Correct Option: A
Explanation:
R is reflexive since $|a-a|=0\leq \dfrac{1}{2}\forall a\in R$.
Also, R is symmetric as $|a-b|\leq \dfrac{1}{2}$
$\Rightarrow |b-a|\leq \dfrac{1}{2}$
But R is not transitive.
e.g.: If we take three numbers $\dfrac{3}{4}, \dfrac{1}{3}, \dfrac{1}{8}$ then $\left|\dfrac{3}{4}-\dfrac{1}{3}\right|=\dfrac{5}{12}\leq \dfrac{1}{2}$ and $\left|\dfrac{1}{3}-\dfrac{1}{8}\right|=\dfrac{5}{24}\leq \dfrac{1}{2}$
But $\left|\dfrac{3}{4}-\dfrac{1}{8}\right|=\dfrac{5}{8} > \dfrac{1}{2}$
Thus, $\dfrac{3}{4}R\dfrac{1}{3}$ and $\dfrac{1}{3}R\dfrac{1}{8}$ but $\dfrac{3}{7}R\dfrac{1}{8}$.

The symbol  '$\geq $'  used in relations is know .............symbol.

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

  1. transitive

  2. reflective

  3. symmetric

  4. asymmetric

Show answer
Correct Option: B
Explanation:
Symbol has pre defined meaning.
Tt is known as reflective symbol.

A ray of light passing through the point $(1, 2)$ is reflected on the $x$-axis at a point $P$ and passes through the point $(5, 3)$. The abscissa of the point $P$ is

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

  1. $3$

  2. $\dfrac {13}{3}$

  3. $\dfrac {13}{5}$

  4. $\dfrac {13}{4}$

Show answer
Correct Option: C
Explanation:
The ray passes through $A(1,2)$ and reflects at $B$ and passes through $(5,3)$

The image of $(5,3)$ with respect to $x-axis$ is $(5,-3)$

The line $AB$ passes through the image of $(5,3)$

The slope of line is $\dfrac{2+3}{1-5}=\dfrac {-5}4$

So the equation of line is $y-2=\dfrac {-5}4\left( x-1\right)$ 

$4y-8=-5x+5$

$\implies 5x+4y-13=0$

The line touches $x-axis $ at $y=0$

$\implies 5x+4(0)-13=0$

$\implies 5x=13$

$\implies x=\dfrac {13}5$

The coordinates of a point P are $(2, 5).$ Given that the image of P under a reflection in the 'x-axis is P, find the coordinates of P.

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

  1. $(-2,-5)$

  2. $(-2, 5)$

  3. $(2,-5)$

  4. $(-5, 2)$

Show answer
Correct Option: C
Explanation:

for reflation in $x-axis$, sing of $y$ coordinets changes and $x-coordinete$ remaing wnstant,

Do,coordinetes of image will be $(2,-5)$

State the following statement is true(T) or false(F).
By lines in geometry, we mean only straight lines.

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

In geometry, line means straight line not a curved line.

When $ABCD$ is reflected over the $y$-axis to ${ A }^{ \prime  }{ B }^{ \prime  }{ C }^{ \prime  }{ D }^{ \prime  }$ , what can be the coordinates of ${ D }^{ \prime  }$ given that D lies in the $1^{st}$ quadrant?

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

  1. $\left( -12,1 \right) $

  2. $\left( -12,-1 \right) $

  3. $\left( 12,-1 \right) $

  4. $\left( 1,12 \right) $

  5. $\left( 1,-12 \right) $

Show answer
Correct Option: A

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 Y axis.

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

  1. $(-1,1)$

  2. $(-1,-1)$

  3. $(1,0)$

  4. $(-1,0)$

Show answer
Correct Option: A
Explanation:

The circle center is $(1,1)$ and reflection over y axis of point $(x,y)\rightarrow (-x,y)$
therefore $(1,1)$ is $(-1,1)$

State whether true/false:
The size of the figure after reflection changes but the lines and angles remains the same.

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

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

The size of the figure does not changes after reflection. So the statement is false.

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.

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

  1. $(1,-1)$

  2. $(1,1)$

  3. $(-1,-1)$

  4. None of the above

Show answer
Correct Option: A
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  $(1,-1)$

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

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

  1. True

  2. False

Show answer
Correct Option: A
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.

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.

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

  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.

Show answer
Correct Option: D
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 .

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.

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

  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

Show answer
Correct Option: B
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 .

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

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

  1. True

  2. False

Show answer
Correct Option: A
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.

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

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

  1. same as

  2. greater than

  3. less than

  4. None of the above

Show answer
Correct Option: A
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

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