Tag: reflection on coordinate axis

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Questions Related to reflection on coordinate axis

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

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

  1. (3, 4)

  2. (- 3, - 4)

  3. (`3, 4)

  4. (3, - 4)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Point P is (-3, 4). First, Mx (reflection in x-axis) changes sign of y-coordinate: (-3, 4) → (-3, -4). Then My (reflection in y-axis) changes sign of x-coordinate: (-3, -4) → (3, -4). The composition My Mx (P) results in (3, -4).

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

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

  1. remain same

  2. increase in the image

  3. decrease in the image

  4. cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
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

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

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

  1. his left hand in the pocket

  2. missing hand

  3. his right hand in the pocket

  4. can't say
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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?

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $\dfrac{3}{7}R\dfrac{1}{8}$.
Multiple choice maths does it look the same? reflection on coordinate axis reflection w.r.t a line reflection

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

  1. $3$
  2. $\dfrac {13}{3}$
  3. $\dfrac {13}{5}$
  4. $\dfrac {13}{4}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $y=0$

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

$\implies 5x=13$

$\implies x=\dfrac {13}5$
Multiple choice maths does it look the same? reflection on coordinate axis reflection w.r.t a line reflection

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?

  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) $
Reveal answer Fill a bubble to check yourself
A Correct answer