Scale factors are important when we talk about making shapes bigger or smaller on a coordinate plane. They determine how much a shape will grow or shrink, which also changes where the shape is and how big it is. Let’s break it down!

What Are Scale Factors?

A scale factor is a number that tells us how to change a shape's size.

• If the scale factor is more than 1, the shape gets bigger.
• If the scale factor is between 0 and 1, the shape gets smaller.

Example of Growing a Shape

Let’s say we have a triangle with points A(1, 2), B(3, 4), and C(2, 1).

If we use a scale factor of 2, we can find the new points for the triangle:

• A'(1 * 2, 2 * 2) = A'(2, 4)
• B'(3 * 2, 4 * 2) = B'(6, 8)
• C'(2 * 2, 1 * 2) = C'(4, 2)

So, the bigger triangle will have points A'(2, 4), B'(6, 8), and C'(4, 2).

Example of Shrinking a Shape

Now let’s look at how to shrink the triangle. If we use the same triangle A(1, 2), B(3, 4), and C(2, 1), and apply a scale factor of 0.5, the new points will be:

• A''(1 * 0.5, 2 * 0.5) = A''(0.5, 1)
• B''(3 * 0.5, 4 * 0.5) = B''(1.5, 2)
• C''(2 * 0.5, 1 * 0.5) = C''(1, 0.5)

So, the smaller triangle will have points A''(0.5, 1), B''(1.5, 2), and C''(1, 0.5).

Important Points to Remember

• Scale factors tell us how to change the size: more than 1 makes it grow, and less than 1 makes it shrink.
• When we use a scale factor, we change the coordinates of each point in a consistent way by multiplying them by that scale factor.

Getting these ideas will help you see how shapes change on the coordinate plane and improve your understanding of geometry!