Reflection about a particular line

Q. The given line segment AB is reflected across the $y$-axis to get the line segment A'B'.

Which of the following statements is not true?

1. Length of AB = Length of A'B'
2. None of the above
3. B and B' have the same $x$-coordinate.
4. B and B' have the same $y$-coordinate.

Q. What is the sequence of transformation followed to get UWXYZ from ABCDE?

1. Rotation (clockwise) around origin, translation and then reflection
2. Rotation (anti clockwise) around origin, translation and then reflection
3. Reflection and then rotation (anti clockwise) around origin
4. Reflection and then rotation (clockwise) around origin

Q. The triangle shown below is the image obtained after the reflection of triangle ABC about the $x$-axis or the $y$-axis.

Which of the following could be the preimage for the given image?

1. 
2. 
3. Neither (A) nor (B)
4. Both (A) and (B)

Q. In the given figure, $\Delta ABC$ is the original shape and $\Delta ADE$ is the transformed shape.

Statement 1: The transformed figure can be obtained from the given set of transformations.
Step 1: Reflection about the $x$-axis
Step 2: Reflection about the $y$-axis
Step 3: Reflection about the $x$-axis

Statement 2: The transformed figure can be obtained from the given set of transformations.
Step 1: ${180}^{\circ }$ counterclockwise
rotation about the origin
Step 2: Reflection about the $x$-axis

Statement 3: The length of the respective sides in the original and the transformed figures will be different.

Statement 4: The angular measurements in the original and the transformed figures will be the same.
Which of the following options is correct?

1. Only statement 1 and statement 4 are correct.
2. Only statement 1 is correct.
3. Exactly 3 statements are correct.
4. Only statement 2 is correct.

Q. If $A=(5,3),$ find $A^{\prime },A^{\prime \prime },$ and $A^{\prime \prime \prime }$ where:
$A^{\prime }$is the reflecting point of $A$ across the $x-$ axis.
$A^{\prime \prime }$ is the reflecting point of $A^{\prime }$ across the $y-$ axis.
$A^{\prime \prime \prime }$ is the reflecting point of $A^{\prime \prime }$ across the $x-$ axis.

1. $A^{\prime }=(5,-3);A^{\prime \prime }=(-5,3);A^{\prime \prime \prime }=(5,3)$
2. $A^{\prime }=(-5,-3);A^{\prime \prime }=(5,3);A^{\prime \prime \prime }=(5,-3)$
3. $A^{\prime }=(5,-3);A^{\prime \prime }=(-5,-3);A^{\prime \prime \prime }=(-5,3)$
4. $A^{\prime }=(-4,-5);A^{\prime \prime }=(5,3);A^{\prime \prime \prime }=(-5,3)$

Q.

The point$B(1,7)$ on the reflection in the line $y=0$ is mapped on$B$. the point $B$ on reflection in the origin is mapped on$B$. find the coordinates of$B$ and $B$. also write down a single transformation that maps $B$ and$B$.

Q. How many of the following statements hold true when a square is reflected about the line $y=x$ in the coordinate plane?
1. The shape of the square changes.
2. The size of the square changes.
3. The coordinates of its vertices changes.
4. The length of its diagonals remains the same.
5. The angular measures of the image and the preimage are the same.
6. The perimeter of the square changes.

1. 6
2. 5
3. 1
4. 3

Q. Two points, A and B, undergo a set of transformations as mentioned below.
\(\begin{array}{|l|l|l|l|}
\hline
\text{Point} & \text{Transformation 1} & \text{Transformation 2} & \text{Transformation 3}\\\hline
A(2, 3) & \text{Translation by 3 units} & \text{Reflection about the \(x\)-axis} & \text{Translation by 2 units in }\\
& \text{toward the left} & & \text{the downward direction}\\\hline
B(3, 2) & \text{Translation by 3 units in} & \text{Reflection about the \(y\)-axis} & \text{Translation by 2 units}\\
& \text{ the downward direction} & & \text{toward the right}\\\hline
\end{array}\)
The line formed by joining the transformed points A and B is reflected about the \(x\)-axis. Which of the following options represents the correct coordinates of the points joined to form the transformed line?