Question

nc.7.g.1 5. identify all images that are scaled copies. for the images that are scaled copies, identify the scale factor

Explanation:

Step1: Recall scale - factor formula

The scale factor \(k\) from the original image to a scaled - copy is found by comparing corresponding side lengths. If the length of a side in the original image is \(a\) and the length of the corresponding side in the scaled - copy is \(b\), then \(k=\frac{b}{a}\).

Step2: Analyze option A

For the vertical side, in the original image it is \(4\) cm and in option A it is \(2\) cm. The scale factor \(k_1=\frac{2}{4}=\frac{1}{2}\). For the horizontal side of the small part, in the original it is \(3\) cm and in option A it is \(1.5\) cm. The scale factor \(k_2 = \frac{1.5}{3}=\frac{1}{2}\). For the long horizontal side, in the original it is \(8\) cm and in option A it is \(4\) cm. The scale factor \(k_3=\frac{4}{8}=\frac{1}{2}\). So option A is a scaled - copy with a scale factor of \(\frac{1}{2}\).

Step3: Analyze option B

For the vertical side, in the original image it is \(4\) cm and in option B it is \(8\) cm. The scale factor \(k_1=\frac{8}{4} = 2\). For the horizontal side of the small part, in the original it is \(3\) cm and in option B it is \(3\) cm. The scale factor \(k_2=\frac{3}{3}=1\). Since the scale factors for different sides are not the same, option B is not a scaled - copy.

Step4: Analyze option C

For the vertical side, in the original image it is \(4\) cm and in option C it is \(\frac{4}{3}\) cm. The scale factor \(k_1=\frac{\frac{4}{3}}{4}=\frac{1}{3}\). For the horizontal side of the small part, in the original it is \(3\) cm and in option C it is \(1\) cm. The scale factor \(k_2=\frac{1}{3}\). For the long horizontal side, in the original it is \(8\) cm and in option C it is \(\frac{8}{3}\) cm. The scale factor \(k_3=\frac{\frac{8}{3}}{8}=\frac{1}{3}\). So option C is a scaled - copy with a scale factor of \(\frac{1}{3}\).

Step5: Analyze option D

For the vertical side, in the original image it is \(4\) cm and in option D it is \(6\) cm. The scale factor \(k_1=\frac{6}{4}=\frac{3}{2}\). For the horizontal side of the small part, in the original it is \(3\) cm and in option D it is \(\frac{9}{2}\) cm. The scale factor \(k_2=\frac{\frac{9}{2}}{3}=\frac{3}{2}\). For the long horizontal side, in the original it is \(8\) cm and in option D it is \(12\) cm. The scale factor \(k_3=\frac{12}{8}=\frac{3}{2}\). So option D is a scaled - copy with a scale factor of \(\frac{3}{2}\).

Answer:

A. Scaled - copy, scale factor \(\frac{1}{2}\)
C. Scaled - copy, scale factor \(\frac{1}{3}\)
D. Scaled - copy, scale factor \(\frac{3}{2}\)