Question

analyze veda draws figures a and b and dilates each figure by a different scale factor. then she uses quotients to compare the area of each image with the area of its original figure. veda says the quotient of the areas is equal to the scale factor. is veda correct? explain.

Explanation:

Step1: Recall area - dilation relationship

Let the scale factor of dilation be \(k\). If the original figure has side - length \(s\) and the dilated figure has side - length \(s'=ks\).

Step2: Calculate areas

The area of the original figure \(A_{1}=s^{2}\) (assuming a two - dimensional figure like a square for simplicity, the result is general for all similar figures). The area of the dilated figure \(A_{2}=(ks)^{2}=k^{2}s^{2}\).

Step3: Find the quotient of areas

The quotient of the area of the dilated figure to the area of the original figure is \(\frac{A_{2}}{A_{1}}=\frac{k^{2}s^{2}}{s^{2}} = k^{2}\).

Answer:

No, Veda is not correct. The quotient of the area of the dilated figure to the area of the original figure is equal to the square of the scale factor, not the scale factor itself.