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The Peculiar Puzzle of Geometrical Transformation-Insights into Transformation Geometry

Updated: Apr 11

Aloha! Excited about Geometric Math? Transformation? Dilation? Well, I am! Transformation is used everywhere! From operating a Mars rover to running a mile, transformation takes the lead. Geometric transformation is a marvel itself. Today, we will dive into the concepts of transformation.

So, What is Geometrical Transformation or Transformation Geometry?

Transformation Geometry is when you move an object from its original position to a new position. The object in the new position is called an image. There are four types of geometric transformations: Dilation, translation, reflection, and rotation.

1.Dilation


Dilation is also frequently known as enlargement. When using the dilation technique we increase or decrease the size of the object. In this process, all the angles remain the same. In other words, the images are similar in shape to the original, but it is a different size. Dilation is unique from other transformations because it moves each point along a straight line. A straight line is drawn from the center of dilation. The distance from the point moved is based on the scale factor. If the scale factor is greater than 1, the size of the image is enlarged. If the scale factor is between 0 and 1 then the image will be smaller than the original.




What is Scale Factor?


To calculate the scale factor you will need to use the formula: image length/original length=scale factor. In other words, image length is the distance of the image from the center of dilation and the original length is the distance of the object from the center of dilation. An example might be if we are facing an illustration showing the two similar triangles ABC and A'B'C'. As we can assume triangle A'B'C' is the dilated version of triangle ABC. D will remain as our center of dilation. Now we can tell that the scale factor is DA'/DA.


scale factor=image length/original length

2.Translation


Translation is when all the points of the original shape are moved in a straight line to draw an image. Translation may seem similar to dilation, but the difference is the shape, size, and orientation remain the same. In translation, every point is moved with the same distance and direction. We represent translation with commands such as “translate 5 units right and 2 units down.”


3.Reflection


When applying geometric reflection all points of the shape are reflected on a line called the axis of reflection or the line of reflection. A reflection technically mirrors the original object. The shape and size are the same as the original object. This is defined as an isometric transformation. Since the orientation is latterly inverted, the image and the original shape are facing opposite directions.


4.Rotation


The rotation transformation is when an object is rotated around a point. When rotation is in use, we decide to move the object clockwise or anticlockwise. The point at which the object is rotated is most commonly known as the center of rotation. The amount we rotate the object is said to be the angle of rotation. Don’t forget to always mention the center, angle, and direction when recording the data.


What are the Geometric Transformation applications in daily life?


You may not have noticed, but everywhere geometric transformation has many applications. Architects may use the dilation transformation when building houses, roads, etc. Translation applies when flying a plane or cooking. Reflection can be related when you look into the mirror or in the footwear industry. Rotation is when you walk or pay a visit to the amusement park.

Aren’t geometric transformations interesting? Now it is thus proven that math can be fun. The geometric transformation has multiple applications in many industries, technologies, and daily life. Right now, you are using the rotation transformation! (heart is circulating blood). Dilation, translation, reflection, and rotation are all mysteries to be uncovered. Credits go to my math teacher who inspired me to write this post. Can’t wait until next time! Adios!


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