Reflections (Leaving Cert Mathematics): Revision Notes

Reflections

What is Reflexion?

Reflection occurs when an object is flipped across a specific line, called the line of reflexion or mirror line, producing an exact replica (mirror image) of the object on the other side of the line. The new shape produced is called the Image.

Key Characteristics of Reflexion:

• The image is the exact same shape and size as the original object.
• Every point on the image is the same distance from the line of reflexion as the corresponding point on the original object.
• The orientation of the image is reversed.

Describing Reflections

To describe a reflexion, you must specify the equation of the line of reflexion or draw the line on the grid.

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Worked Example 1: Reflection in a Vertical Line

Reflect the blue object in the red line, given by the equation $x=2$:

1. Identify the line of reflection: The line $x=2$ is a vertical line passing through the grid where $x=2$.
2. Reflect each point of the blue object across the line $x=2$.
3. Draw the reflected object (purple) on the other side of the line, ensuring each point is the same distance from the line as the corresponding original point. Notice: Every point on the purple object is the same distance from the line of reflexion as the corresponding point on the blue object.

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Worked Example 2: Reflection in a Diagonal Line

Reflect the blue object in the red line, given by the equation $y=x$:

4. Identify the line of reflection: The line $y=x$ is a diagonal line where every $x$ value equals its corresponding $y$ value.
5. Reflect each point of the blue object across the line $y=x$.
6. Draw the reflected object (purple) on the other side of the line, ensuring each point is equidistant from the line. Notice: Reflecting across a diagonal line like $y=x$ can be more challenging, but the principle remains the same: each point on the reflected object is the same distance from the mirror line as the corresponding original point.