Question

What is the rule for the reflection? rx-axis(x, y) → (â€"x, y) ry-axis(x, y) → (â€"x, y) rx-axis(x, y) → (x, â€"y) ry-axis(x, y) → (x, â€"y).

Answer 1

The rule for the reflection is explained below. The correct option will be x-axis (x, y) = (x, -y).

In real life, we think of a reflection as a mirror image, like when we look at own reflection in the mirror.

This idea of reflection correlating with a mirror image is similar in math.

Reflection Over the X Axis

A reflection of a point, a line, or a figure in the X axis involved reflecting the image over the x axis to create a mirror image.

In this case, the x axis would be called the axis of reflection.

The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.

When point P with coordinates (5,4) is reflecting across the X axis and mapped onto point P’, the coordinates of P’ are (5,-4).

Notice that the x-coordinate for both points did not change, but the value of the y-coordinate changed from 4 to -4.

Reflection Over the Y Axis

A reflection of a point, a line, or a figure in the Y axis involved reflecting the image over the Y axis to create a mirror image.

In this case, the Y axis would be called the axis of reflection.

The rule for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the y-value the same.

when point P with coordinates (5,4) is reflecting across the Y axis and mapped onto point P’, the coordinates of P’ are (-5,4).

Notice that the y-coordinate for both points did not change, but the value of the x-coordinate changed from 5 to -5.

Hence the correct option is r x-axis(x, y) = (x, -y).

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