Question

problems 6 - 7
here is a polygon.
heres your polygon from the previous screen.
what is the scale factor from the original polygon to the scaled copy that has a perimeter of 10 units?
what is the scale factor from the scaled copy back to the original polygon?

Explanation:

Step1: Count original perimeter

Count the side - lengths of the original polygon. The original polygon has a perimeter of 20 units (by counting each 1 - unit side - length around the shape).

Step2: Calculate scale factor to scaled copy

The formula for the relationship between perimeters and scale factor \(k\) is \(P_{scaled}=k\times P_{original}\). We know \(P_{scaled} = 10\) and \(P_{original}=20\). So, \(k=\frac{P_{scaled}}{P_{original}}=\frac{10}{20}=\frac{1}{2}\).

Step3: Calculate scale factor from scaled copy back to original

The scale factor from the scaled copy back to the original is the reciprocal of the scale factor from the original to the scaled copy. If the scale factor from original to scaled is \(k_1=\frac{1}{2}\), then the scale factor from scaled to original \(k_2 = 2\).

Answer:

The scale factor from the original polygon to the scaled copy is \(\frac{1}{2}\).
The scale factor from the scaled copy back to the original polygon is 2.