Question

Which of the following is a single reflection of figure N over the y-axis to form N'?

A) Reflect N over the y-axis to form N'
B) Rotate N 90 degrees counterclockwise to form N'
C) Translate N two units to the right to form N'
D) Reflect N over the x-axis to form N'

Answer 1

The correct transformation to create a mirror image of figure N across the y-axis to form N' is option A, reflecting N over the y-axis. This will produce figure N' with the same y-coordinates as figure N but with opposite x-coordinates. So, the correct answer is A) Reflect N over the y-axis to form N'.

Step-by-step explanation:

The question pertains to performing transformations on a geometric figure in the coordinate plane.

Specifically, a single reflection of figure N over an axis to form N'. The correct choice for reflecting a figure over the y-axis to form its mirror image is option A) Reflect N over the y-axis to form N'.

This transformation will produce a figure N' that is a mirror image of the original figure N across the y-axis.

When reflecting over the y-axis, each point of figure N will have the same y-coordinate in figure N', but the x-coordinate will have the opposite sign.

So, the correct answer is A) Reflect N over the y-axis to form N'.

Answer 2

A) Reflect N over the y-axis to form N', as this transformation involves changing the sign of the x-coordinates while leaving the y-coordinates unchanged, resulting in the proper reflection.

Step-by-step explanation:

When reflecting a figure over the y-axis, each point (x, y) in the original figure becomes (-x, y) in the reflected figure. In this case, reflecting figure N over the y-axis means changing the sign of the x-coordinates while keeping the y-coordinates unchanged. The process can be represented as follows:

`\[ N' = \{( -x_1, y_1), ( -x_2, y_2), \ldots, ( -x_n, y_n)\} \]`

So, for example, if a point in N is (3, 4), the corresponding point in N' after reflecting over the y-axis would be (-3, 4). Therefore, option A) Reflect N over the y-axis to form N' is the correct choice.

This transformation is distinct from the other options. Option B involves a counterclockwise rotation, option C involves a translation to the right, and option D involves a reflection over the x-axis. These transformations would alter both the x and y coordinates of the points in figure N, making them incorrect for the given question.

In conclusion, the correct transformation to form N' from figure N is a reflection over the y-axis, as described in option A.