Question

as you answer the questions below, consider the physical connection between scale factors and resized objects.

1. can you use 0 as a scale factor to create a distinct object in a similar set? explain why or why not.

Explanation:

A scale factor of \(0\) would multiply all dimensions of an object by \(0\). This would result in an object with zero length, width, and height (i.e., a degenerate object - it would collapse to a single point). A distinct object in a similar set must have non - zero dimensions (so that it has a shape and size that can be compared to other objects in the set). Since a scale factor of \(0\) does not produce a non - degenerate object with recognizable shape and size (as required for similarity in a set of objects), it cannot be used.

Answer:

No. A scale factor of \(0\) would make all dimensions of the object \(0\) (e.g., if the original object has a side length \(l\), the new side length \(l_{new}=0\times l = 0\)). The resulting “object” is a point (no distinct shape or size like other non - zero scale factor resized objects in a similar set), so it is not a distinct object in the set.