Question

1. figure 2 is a scale drawing of figure 1. figure 1 has an area of 6 square units, and figure 2 has an area of 294 square units. what scale factor relates figure 2 to figure 1? explain how you know.

Explanation:

Step1: Recall area - scale factor relationship

If the scale factor of two similar figures is \(k\), the ratio of their areas is \(k^{2}\). Let the scale factor from figure 1 to figure 2 be \(k\). Then \(\frac{\text{Area of figure 2}}{\text{Area of figure 1}}=k^{2}\).

Step2: Calculate the ratio of the areas

We know that the area of figure 1 is \(A_1 = 6\) square units and the area of figure 2 is \(A_2=294\) square units. So, \(k^{2}=\frac{A_2}{A_1}=\frac{294}{6}=49\).

Step3: Find the scale factor

Take the square - root of \(k^{2}\). Since \(k^{2}=49\), then \(k = 7\) (we take the positive value because a scale factor represents a ratio of lengths and is non - negative).

Answer:

7