13.1 Enlargements and reductions with scale factors
You’re given this project for art class. You’re asked to draw your most favorite building in town in a short bond paper. The teacher specified that you need to scale the drawing to the size of the paper. Ordinarily you would just draw what you see not really paying attention to the actual scale of the drawing and later on realize that you are able to draw the building in a much smaller scale. If you want to know how to scale correctly then you better look at this chapter thoroughly.
Scaling isn’t just in drawing, but also in making models for buildings, for machines and a lot of other things. The smaller versions are created to represent what the lifesize version would look like. To give you more idea about scaling then you should check out Scale City, this video shows small figures in the real world.
Now, in this chapter, we would start with learning the enlargement and reduction of a particular subject using a scale factor. Earlier you were asked to scale your drawing to the size of the paper, which means the scale factor of your drawing should be based on the size of the paper. For this first part of this chapter, we will be using a grid paper to fully grasp what scaling really means. We will learn how to adjust sizes and also to solve for the scale factor.
In section 2, we will then apply the scale factor in order to make a copy of a particular object that would be of proportion to the original. Knowing whether you are able to make a proportional copy would teach you that this characteristic of proportionality can be applied in mathematical problems especially those involving Geometry. We are able to check whether your drawings are good scaling of the original by looking at the proportion of the sizes.
Applying what we will learn from the first parts of the chapter, in section 3, we would be learning how to determine whether a pair of triangles is proportional to each other by looking at corresponding sides and corresponding angles. Knowing the Pythagorean theorem and it’s application, plus looking at the measurements of the corresponding sides and angles given, we would be able to determine if they are proportional with each other.
After that, we would then branch out to looking at similar polygons. In section 4 we would be learning all about similar polygons. These shapes have proportional sides and angles, much like how similar triangles are.
Enlargements and reductions with scale factors
Basic concepts:
 Ratios
 Rates
 Proportions
Lessons

1.
Redraw the letters below using a scale factor of 2.

3.
The ratio of the length to the width of a window is 3:2. If the window is 8 m wide, what are the dimensions of the window that has a scale factor of: