Question

A point undergoes a certain transformation. The initial coordinates, the final coordinates, and the transformation the point undergoes are mentioned in each option.
Which of the following options contains the correct combination of the initial coordinates, the final coordinates, and the transformation followed?

• A. All of the above
• B. $\begin{array}{ccc}\text{Initial coordinates}& \text{Final coordinates}& \text{Transformation}\\ (2,4)& (2,-4)& \text{Reflection about the}\\ & & x\text{-axis}\end{array}$
• C. $\begin{array}{ccc}\text{Initial coordinates}& \text{Final coordinates}& \text{Transformation}\\ (2,4)& (-2,4)& \text{Reflection about the}\\ & & y\text{-axis}\end{array}$
• D. $\begin{array}{ccc}\text{Initial coordinates}& \text{Final coordinates}& \text{Transformation}\\ (2,4)& (4,4)& \text{Translation of 2 units}\\ & & \text{toward the right}\end{array}$

Answer 1

The correct option is A All of the above

Option A:
Given: The initial coordinates of the point are (2, 4).
The transformation that happens when the given point is translated 2 units toward the right is shown in the image given below.

We can observe from the figure shown above that the final coordinates of the point after the given transformation are (4, 4).
Hence, the given option contains the correct combination of the initial coordinates, the final coordinates, and the transformation followed.
Option B
Given: The initial coordinates of the point are (2, 4).
The transformation that happens when the given point is reflected about the $x$-axis is shown in the image shown below.


We can observe from the figure shown above that the final coordinates of the point after the given transformation are (2, -4).
Hence, the given option contains the correct combination of the initial coordinates, the final coordinates, and the transformation followed.
Option C
Given: The initial coordinates of the point are (2, 4).
The transformation that happens when the given point is reflected about the $y$-axis is shown in the image shown below.

We can observe from the figure shown above that the final coordinates of the point after the given transformation are (-2, 4).
Hence, the given option contains the correct combination of the initial coordinates, the final coordinates, and the transformation followed.
$\to$ Option D is correct.