Question

is scale factor decides the size of image or not

Answer 1

In two similar geometric figures, the ratio of their corresponding sides is called the scale factor. To find the scale factor, locate two corresponding sides, one on each figure. Write the ratio of one length to the other to find the scale factor from one figure to the other. In this example, the scale factor from the blue figure to the red figure is 1.6 : 3.2, or 1 : 2. This means that for one unit of length on the blue figure, there are two units of length on the red figure. The scale factor from the red figure to the blue figure is 3.2 : 1.6, or 2 : 1.

It is important to notice two things about the scale factor:

The scale factor from the first figure to the second is always the reciprocal of the scale factor from the second figure to the first.

If you begin with the smaller figure, your scale factor will be less than one. If you begin with the larger figure, your scale factor will be greater than one.

Ask yourself, 'Am I comparing a larger figure to a smaller figure, or a smaller figure to a larger?' This can help you check your work.

Using the Scale Factor

If two figures are similar, then you can relate different characteristics of the figure by using the scale factor. As an example, think of two squares that are similar. One has a side length of 2 inches and another has a side length of 4 inches. This gives a scale factor of 1 : 2 from the small square to the large square.

These two similar squares have a scale factor of 1 : 2 from the small square to the large square.

To obtain the side length of one square given the side length of the other, you can multiply or divide by the scale factor. Let's see this with the squares shown above.

Suppose you are told that the smaller square has a side length of 2 inches and the scale factor from the smaller to the larger is 1 : 2. Remember, this means that 1 inch on the smaller square is 2 inches on the larger square. If we multiply by the scale factor, 1/2, we will get a smaller number. So we must 'divide' by the scale factor to get a larger number.





We can see that this result matches the picture.

To obtain the perimeter of one square given the perimeter of the other, you can multiply or divide by the scale factor. The smaller square has a perimeter of 8 inches. We want to find the perimeter of the larger square. We will once again need to divide by the scale factor of 1 : 2.