Answer to Question #125965 in Geometry for Nomzamo

Question

(1) Describe the key concepts in transformation geometry. Use illustrations/drawings or examples to support your argument in each case.

(2) Think of any situation in your everyday life in which you can experience transformation geometry. Illustrate your answers. 

Answer 1

1.

a)Rotation

This involves moving an object about a fixed point without altering with the shape or the size of the object. Rotation of an object involves moving that object about a fixed point. To rotate a preimage, you can use the following rules. To rotate an object 90° the rule is (x, y) → (-y, x). You can use this rule to rotate a preimage by taking the points of each vertex, translating them according to the rule and drawing the image. For example, if the points that mark the ends of the preimage are (1, 1) and (3, 3), when you rotate the image using the 90° rule, the end points of the image will be (-1, 1) and (-3, 3).

b)Translation

Translation involves moving an object without altering with either the shape, size or orientation of the object. It is always performed by moving the preimage by the requested number of spaces.

For example move the below figure to the right seven spaces. If you take each vertex of the triangle and move the requested number of spaces, then draw the new triangle. This will be your translated image:

The mathematical way to write a translation is the following: (x, y) → (x + 7, y + 0), because you have moved seven positive spaces in the x direction and no spaces moved in the y direction. A translation can be either in any direction depending on the demands of the question.

c)Reflection

This involves flipping of an object over a line of reflection. The line of reflection can either be horizontal, vertical, or be sloped in any direction. The object abc is reflected by the line of reflection into a'b'c' as illustrated below.

2. In the real-life situation, I experience a reflection in the mass production of shoes and spectacle frames. Similarly, translation has made it possible to communicate and share important information across language borders. For example, translation has enabled the spread of religion and sharing of knowledge across the globe. Rotation is where we (us) holding hands in a circle while walking in the same direction.