Question

from unit 2, lesson 3
jada claims that ( bcd ) is a dilation of ( bcd ) using ( a ) as the center of dilation.
what are some ways you can convince jada that her claim is not true?

Explanation:

Step1: Check if lines from center pass through original points

In a dilation with center \(A\), lines \(AB'\) should pass through \(B\), \(AC'\) through \(C\), and \(AD'\) through \(D\). But in the given figure, lines from \(A\) to \(B',C',D'\) do not pass through \(B,C,D\) respectively.

Step2: Check if ratios of distances are equal

For a dilation with center \(A\), the ratio \(\frac{AB'}{AB}=\frac{AC'}{AC}=\frac{AD'}{AD}\) should hold. By measuring (if possible) or visual inspection (assuming non - proportional lengths), these ratios are not equal.

Answer:

Jada's claim is not true because 1) Lines from center \(A\) to \(B',C',D'\) do not pass through \(B,C,D\) (a property of dilation: all points and their images lie on lines through the center of dilation). 2) The ratios of distances from center \(A\) to corresponding points (e.g., \(\frac{AB'}{AB}\), \(\frac{AC'}{AC}\), \(\frac{AD'}{AD}\)) are not equal (another property of dilation: a constant scale factor \(k=\frac{\text{distance from center to image}}{\text{distance from center to original point}}\) for all points).