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# Vertical Flip|Definition & Meaning

## Definition

A **vertical flip** is the same drawing of any item or figure but **flipped vertically** so that it appears **upside-down**. It is sometimes called a “**water reflection**.” In the reflection, the** highest point** appears as the **lowest point**, while the **lowest point** appears as the **highest**. Furthermore, this applies to anything ranging from an **item** to a **linear graph**.

**Vertical reflection** or **vertical flipping** is commonly used to **simplify** things by looking at them from a different perspective. **Reflection** has numerous uses in mathematics, **real-life architecture,** and graphs as well. Moreover, it’s fairly easy to **redraw** a reflection of a graph and this helps in finding **solutions** to **problems** quickly.

Vertical flipping is a type of reflection that reflects a figure or a graph with respect to the horizontal line. Its **properties** are very **significant** in its **real-life applications,** which further makes it much more viable in **transformations** and graphical conversions such as **Laplace** or **Fourier transforms.**

## Properties of Vertical Flipping

A vertical flipping consists of a horizontal reference line, “**Line of Reflection**,” that is **parallel** to the **x-axis** and converts the image into an **identical** but **vertically inverted image.** Every point on the image is equidistant to the line and hence this is a very important property of a vertical reflection. Furthermore, if the line of reflection is not parallel to the x-axis, we will not achieve a properly vertically flipped image on the other side of the line.

Moreover, the **reflected version** of the image will look **upside-down** as compared to the original figure due to each point of the image being at an **equal distance** from the **line of reflection** as the same point on the original image. This property helps in **photography** such as **taking pictures** of a lake and a mountain that has a vertical reflection made on the lake.

In general, these reflections also act in creating new and easier images using the **symmetry concept,** where one part of the figure is **identical** but **mirrored** to the other part of the figure which makes it a complete figure when coupled together. These figures have a line of reflection in the **midpoint** of the figures where each side is identical to the other. The line of reflection can be either **vertical** or **horizontal** given that the sides of the figure are identical in that case.

## Comparisons With Horizontal Flipping

The **concept** of **reflections** is the same for horizontal flipping as for vertical flipping. The only **difference** that is observed in the two types of flipping is the **line of reflection. Vertical flipping** has a line of reflection that is parallel to the **x-axis,** whereas the line of reflection is parallel to the **y-axis** for **horizontal flipping.**

Horizontal flipping is usually seen in our daily lives in **mirrors.** The figure that we see of ourselves in a **mirror** is **inverted horizontally** and hence, this is the reason our left-hand looks like a right and our right-hand looks as if it is left in the mirror. The line of reflection of the mirror is the plane parallel to the mirror and it is the reason why the figure that we see is inverted.

Moreover, **horizontal reflection** is also used to **transform** graphs and to help find their solution by looking at them from a different perspective. This application is **similar** to what vertical flipping helps in doing.

Additionally, besides horizontal flipping, other transformations such as **rotation, transformation,** and **dilation** play a similar role in helping find the **implicit meanings** and solutions to different figures or graphs.

## Construction of a Graph Undergoing a Vertical Flip

To construct a vertical reflection of a graph alongside an **x-axis** as the **line of** **reflection,** all you need is to **multiply** the **y-coordinates** of the **graph** by **-1.** The condition here is that you have graph paper available and the line of reflection is the x-axis. In case we have a line of reflection parallel to the x-axis, we would require to follow the steps below:

- First,
**measure**and**draw**a**line**from**each point**of the graph**perpendicularly**to the line of reflection. - After that, draw a
**perpendicular line**of the**same length**on the other side of the line of reflection - Finally,
**join**all the**points**that have been drawn on the graph on the**opposite side**of the line of reflection.

By this process, we would be able to achieve a **vertically flipped version** of the graph or a figure on the other side of the line of reflection.

**An Example Depicting the Usage of a Vertical Flip**

We are given a **linear graph** **“y = 2x +1”** in the positive half of the **x-axis. Find** and **draw** the **vertical reflection** of the **graph,** where the **line of reflection** is the **x-axis**

**Solution**

To find the reflection of the graph **y = 2x + 1, **all we require is to **invert** the y-coordinates of the graph to **acquire** the **reflection** of the graph at the line of reflection being the x-axis.

This graph is a linear equation that can be generalized by the formula,** y = mx + c**. The **y-intercept “c,”** is equal to **+1** in this curve. For the reflected graph, the y-intercept c` will be equal to **c****` = -1 * ****c = -1(1) = -1**. Hence, the c is equal to -1.

Furthermore, since it is a reflection, the graph must have a **negative proportionality** as compared to the original line, which will cause the x-axis to be equidistant from both graphs. Hence, the **gradient “m”** must be **multiplied** by **-1** as well. This value will be equal to:

m’ = 2x * (-1)

m’ = -2x

Thus, the **resulting reflected line** will have the formula **“y = -2x – 1.”**

*All the graphs and figures were created using GeoGebra.*