Question

1 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

When a figure is dilated by a scale factor \(k\), if the original area is \(A_1\) and the new - area is \(A_2\), the formula for the relationship between the areas of the original and dilated figures is \(A_2=k^{2}A_1\).

Step2: Calculate the quotient of the areas

The quotient of the area of the dilated figure (\(A_2\)) and the area of the original figure (\(A_1\)) is \(\frac{A_2}{A_1}\). Substituting \(A_2 = k^{2}A_1\) into the quotient, we get \(\frac{A_2}{A_1}=\frac{k^{2}A_1}{A_1}=k^{2}\).

Answer:

Veda is not correct. The quotient of the area of a dilated figure and the area of its original figure is equal to the square of the scale factor, not the scale factor itself.