Transformation Geometry

This task is aimed in showing its readers how a figure may be transformed and be connected with the preliminary points, and how such points might be altered as a shift is made. This provides us an idea that an image might be turned or moved. Despite time and location, this provides the chance for individuals to really use a system in geometry in accurately doing things. Even employees in a garment business utilize such improvement. This is called a line reflection.

Line reflection is used in cutting the pieces of garment faster and more precisely, and making certain that it is still the best fit. For this job, I picked a figure that is rectangle-shaped fit. I utilized this figure to show the x and y-axis, and translated the initial figure by making a 90-degree counterclockwise rotation. What is transformation? Change is defined as the modification in position, while having numerous points. Airplanes likewise have changes, just as the objects experience a change in position.

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There are also times that the points do not move, and stay in a fixed position. Reflection, on the other hand, is referred to as the aircraft transformation. This implies that the points in the plane are changed or relocated to another position. The exact same outright value is used in the reflection of a point. These are normally altered from positive to negative. The shown image appears on the plane on the line. For this, I have actually pointed the y-axis in the initial image.

Also, I have observed that the slope was changed from favorable to negative and negative, then negative to favorable.

Sadly, the slope did not change when the original was utilized. In the coordinate airplane, the origin is 0 (0,0), where all points are possible. An ABCD image may be viewed as A"B"C"D. The reflection of the line over the y-axis is altered, making the slope modification too. Take for example, I have a rectangle-shaped shaped item. AB is a straight line, and I will use its points to reveal the modifications made from the initial to the reflection. Point A has coordinates of (3,4) and point B has (8,12). For that reason, 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.