 # Transformation Geometry Essay

This project is aimed in showing its readers how a figure may be transformed and be associated with the initial points, and how such points may be altered as a shift is made. This gives us an idea that an image may be rotated or moved. Regardless of time and place, this gives the opportunity for people to actually use a system in geometry in accurately doing things. Even workers in a garment company make use of such transformation. This is called a line reflection.

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Line reflection is used in cutting the pieces of garment faster and more accurately, and making sure that it is still the right fit. For this project, I chose a figure that is rectangular in shape. I used this figure to show the x and y-axis, and translated the original figure by making a 90-degree counterclockwise rotation. What is transformation? Transformation is defined as the change in position, while having numerous points. Planes also have transformations, just as the objects experience a change in position.

There are also times that the points do not move, and remain in a fixed position. Reflection, on the other hand, is known as the plane transformation. This means that the points in the plane are transformed or moved to another position. The same absolute value is used in the reflection of a point. These are usually changed from positive to negative. The reflected image appears on the plane on the line. For this, I have pointed the y-axis in the original image. Also, I have observed that the slope was changed from positive to negative and negative, then negative to positive.

Unfortunately, the slope did not change when the original was used. In the coordinate plane, the origin is 0 (0,0), where all points are possible. An ABCD image may be seen as A”B”C”D. The reflection of the line over the y-axis is changed, making the slope change as well. Take for example, I have a rectangular shaped object. AB is a straight line, and I will use its points to show the changes made from the original to the reflection. Point A has coordinates of (3,4) and point B has (8,12). Therefore, the equation is y=x+1.

The reflection, on the other hand, for point A becomes (-3,7) and point B becomes (-8,12). This changes the equation to y=-x+4. Furthermore, the slope for the reflection of point AB remains the same. Unfortunately, the absolute is changed with the Y intercept, changing it from negative to positive, then positive to negative. For example, AB is equal to y=x+4, with point A being (3,7). The point is changed to y=x – 4 after reflection. Reflection of segment AB over X-axis changes the slope and they intercept from positive to negative and negative to positive.

For example, segment AB origin A was (3, 7) and B (8, 12) and its equation Y= X+4. After reflecting over X-axis it become A’ (3,-7) and B’ (8,-12) and its equation Y= -X – 4. It is also evident that rotation be defined. So what is rotation? Rotation is defined as the transformation of a coordinate system in which the new axes have a fixed angular displacement from their original position while the origin remains the same. After the rotations, I observed several changes. The negative slope changed to positive, and the positive slope was changed to negative.

In addition to this, the y-intercept were also changed, from being positive, they became negative, and vice versa. Translation on the other hand is defined as the transformation or change in position that resulted to a slide with no tum. Although there was a translation, the y intercept and the slope remained the same. This project aimed to show its readers the effects of applying reflection, rotation, and translation into a shape. This also showed the relationship between the original shape and the original point.