Question

activity 3: scaled rectangles
ere is a picture of rectangle r, which has been evenly divided into smaller
rectangles. two of the smaller rectangles are labeled b and c.

1. is b a scaled copy of r? if so,

what is the scale factor?

1. is c a scaled copy of b? if

so, what is the scale factor?

1. is c a scaled copy of r? if

so, what is the scale factor?

Explanation:

Step1: Check if B is a scaled copy of R

Assume the side - length of the small squares is \(1\). Let's assume the length and width of rectangle \(R\). Suppose the length of \(R\) is \(4\) (number of small squares along the length) and the width is \(4\) (number of small squares along the width). The length of \(B\) is \(4\) and the width is \(2\). Since the ratio of lengths (and widths) of corresponding sides is constant. The scale factor from \(R\) to \(B\): if we consider the width (or length), \(R\) has a width of \(4\) and \(B\) has a width of \(2\). The scale factor \(k=\frac{2}{4}=\frac{1}{2}\). So \(B\) is a scaled copy of \(R\) with scale factor \(\frac{1}{2}\).

Step2: Check if C is a scaled copy of B

The width of \(B\) is \(2\) and the width of \(C\) is \(1\). The length of \(B\) is \(4\) and the length of \(C\) is \(1\). The scale factor from \(B\) to \(C\): \(k = \frac{1}{2}\) (for both length and width). So \(C\) is a scaled copy of \(B\) with scale factor \(\frac{1}{2}\).

Step3: Check if C is a scaled copy of R

The scale factor from \(R\) to \(C\): if \(R\) has length \(4\) and \(C\) has length \(1\), \(k=\frac{1}{4}\) (also for width, since \(R\) has width \(4\) and \(C\) has width \(1\)).

Answer:

1. Yes, \(B\) is a scaled copy of \(R\) and the scale factor is \(\frac{1}{2}\).
2. Yes, \(C\) is a scaled copy of \(B\) and the scale factor is \(\frac{1}{2}\).
3. Yes, \(C\) is a scaled copy of \(R\) and the scale factor is \(\frac{1}{4}\).