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## Topics Covered in Reflection

- Position of a Point in a Plane
- Reflection of a Point in a Line
- Reflection of a Point in the x-axis
- Reflection of a Point in the y-axis
- Reflection of a Point in the Origin
- Reflection of a Point in a Line Parallel to the x-axis
- Reflection of a Point in a Line Parallel to the y-axis
- Problems on Reflection in the x-axis or y-axis
- Invariant Points for Reflection in a Line
- Reflection in Lines Parallel to Axes
- Worksheet on Reflection in the Origin

### Reflection – Definition

In maths, reflection is defined as a mapping from Euclidean space to itself. It has a set of fixed points that set is called axis or plane of reflection. In geometry or coordinate geometry, the reflection is known as a flip.

A reflection is a transformation of the figure representing a flip. The reflected figure may be a plane, line, or point. The original image is known as a pre-image and its reflected image is called an image.

### Reflection in the Coordinate Plane

The reflection in the coordinate plane may be in reference to X-axis and Y-axis.

#### Reflection of a Point in the x-axis

In the case of reflection over the x-axis, the point is reflected across the x-axis. The x-coordinates remain the same and the y-coordinates will be transformed into their opposite sign.

The reflection of the point (x, y) across the x-axis is (x, -y)

#### Reflection of a Point in the y-axis

In the case of reflection over the y-axis, the point is reflected across the y-axis. The y-coordinates remain the same and the x-coordinates will be transformed into their opposite sign.

The reflection of the point (x, y) across the x-axis is (-x, y)

#### Reflection in a point

A reflection point happens when a figure is built around a solitary point known as the mark of reflection or focus of the figure. For each point in the figure, another point is seen as straightforwardly inverse to it on the opposite side. Under the mark of reflection, the figure doesn’t change its size and shape.

#### Reflection in Origin

In a plane, we can use any point as the point of reflection and the most commonly used point is the origin.

The point of reflection in origin (0, 0), the image of the point (x, y) is (-x, -y).

### Examples Problems on Reflection

**Example 1.**

Write the coordinates of the image of the point (5, -9) when reflected in the x- axis.

**Solution:**

Given that the point is (5,-9)

The reflection image of (5,-9) is (-5,9).

**Example 2.**

Write the coordinates of the image of the point (-6, 2) when reflected in the y-axis.

**Solution:**

Given that the point is (-6, 2)

The reflection image of (-6, 2) is (6, -2).

**Example 3.**

Find the reflection of the point P(0,7) in the origin.

**Solution:**

Given that the point is P(0,7)

The reflection of the point H (0, 7) in the origin is the point H’ (0, -7)

**Example 4.**

Write the coordinates of the image of the point (3, -2) when reflected in the x-axis.

**Solution:**

Given that the point is (3,-2)

The reflection image of (3,-2) is (-3,-2).

**Example 5.**

Find the reflection of the point (0,2) in the origin.

**Solution: **

The reflection of the point (0, 2) in the origin is (0, -2).

### FAQs on Reflection

**1. What is a reflection in maths for example?**

In a reflection over the line y = x, the x- and y-coordinates simply switch positions.

**2. How do you do reflections in math?**

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite.

**3. What are the types of reflection in math?**

There are four types of transformations: translations, reflections, dilations, and rotations. Reflections in transformations involve flipping a shape or figure over a line of reflection, a point of reflection, or a plane of reflection.