Question

level 7, benchmark 1, session 2
modify figure b so that the scale factor from figure a to figure b is 3/2.
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Explanation:

Step1: Analyze the original side - lengths

Assume the side - lengths of figure A. For example, if we consider the horizontal side \(ST\) of figure A. Suppose in figure A, the length of \(ST = 2\) units.

Step2: Use the scale - factor formula

The scale - factor \(k=\frac{\text{length in figure B}}{\text{length in figure A}}\). Given \(k = \frac{3}{2}\). If \(x\) is the length in figure B and \(y\) is the length in figure A, then \(x=k\times y\). So if \(y = 2\), then \(x=\frac{3}{2}\times2=3\). We need to adjust all corresponding side - lengths of figure B (such as \(R - S\), \(S - T\), \(T - U\), \(U - Q\), \(Q - R\)) by multiplying their original lengths (from figure A) by \(\frac{3}{2}\).

Answer:

Multiply each side - length of figure A by \(\frac{3}{2}\) to get the corresponding side - lengths of figure B. For example, if a side of figure A has length \(l\), the corresponding side of figure B has length \(\frac{3}{2}l\). Then redraw figure B with the new side - lengths.