(4 2) Reflected Over Y Axis

Suzhoumeite

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Jul 03, 2024

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Reflecting (4, 2) over the Y-Axis

What is Reflection?

In geometry, reflection is a type of transformation that involves flipping a figure over a line, known as the line of reflection. The resulting image is a mirror image of the original figure, created by flipping it over the line of reflection.

Reflecting (4, 2) over the Y-Axis

Let's reflect the point (4, 2) over the Y-axis. The Y-axis is a vertical line that passes through the origin (0, 0).

To reflect a point over the Y-axis, we need to change the sign of the x-coordinate. In other words, we need to multiply the x-coordinate by -1.

Original Point: (4, 2)

The original point is (4, 2), which means the x-coordinate is 4 and the y-coordinate is 2.

Reflected Point: (-4, 2)

To reflect the point over the Y-axis, we change the sign of the x-coordinate:

x-coordinate: 4 → -4 y-coordinate: 2 (remains the same)

The reflected point is (-4, 2).

Graphical Representation

Here's a graphical representation of the reflection:

Before Reflection:

  (4, 2)
  |
  |
  Y-axis

After Reflection:

  (-4, 2)
  |
  |
  Y-axis

In this diagram, the original point (4, 2) is reflected over the Y-axis to produce the image point (-4, 2).

Conclusion

In conclusion, reflecting the point (4, 2) over the Y-axis results in the point (-4, 2). This is achieved by changing the sign of the x-coordinate, while keeping the y-coordinate the same.