As a geometry expert, I can help you understand how to enlarge a shape by a negative scale factor. When we talk about scaling a shape, we are essentially changing its size while maintaining its proportions. A scale factor is a number that determines how much the shape will be scaled. A positive scale factor means the shape will be enlarged, while a negative scale factor indicates that the shape will be both enlarged and reflected across a certain axis.

Let's consider the example given: a rectangle WXYZ, which we want to enlarge by a scale factor of -2, with the center of enlargement being the origin (0,0). Here's how you can do it step by step:


1. Identify the Shape and Its Points: First, you need to know the coordinates of the rectangle WXYZ. Let's assume W is at (0,0), X is at (a,0), Y is at (a,b), and Z is at (0,b), where 'a' and 'b' are the lengths of the sides of the rectangle.


2. Understand the Negative Scale Factor: A negative scale factor of -2 means that each point of the rectangle will be moved twice the distance from the origin in the opposite direction along both axes.


3. Apply the Scale Factor: To apply the negative scale factor, you multiply the coordinates of each point by -2. This will give you the new coordinates of the enlarged rectangle:
- Point W: (0,0) becomes (0,0) because multiplying by -2 and then by -1 (to get the opposite direction) results in the same point.
- Point X: (a,0) becomes (-a,0) after multiplying 'a' by -2.
- Point Y: (a,b) becomes (-a,-b) after multiplying 'a' and 'b' by -2.
- Point Z: (0,b) becomes (0,-b) after multiplying 'b' by -2.


4. Reflect Across the Origin: Since the scale factor is negative, the resulting shape will be a reflection of the original shape across the origin. This means that the new rectangle will have its corners at the points (-a,0), (-a,-b), (0,-b), and (0,0).


5. Visualize the Transformation: Imagine the original rectangle being flipped over the origin and then enlarged by a factor of 2. The new shape will be a mirror image of the original, but each side will be twice as long.


6. Conclusion: The process of enlarging a shape by a negative scale factor involves both a reflection across an axis and an enlargement. In this case, the axis is the origin, and the shape is reflected and enlarged simultaneously.

Now, let's move on to the translation of the explanation.

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Negative scale factors. An enlargement using a negative scale factor is similar to an enlargement using a positive scale factor, but this time the image is on the other side of the centre of enlargement, and it is upside down. Enlarge the rectangle WXYZ using a scale factor of - 2, centred about the origin.read more >>