Question

scale factor:
rule:
scale
rule:
which of the following is not a true statement about the dilation shown at the right?
a. the dilation represents an enlargement.
b. the ratio of (\frac{hi}{hi} = \frac{ij}{ij}).
c. the dilation can be represented by ((x, y) \to (2x, 2y)).
d. the dilation changed the orientation of the figure.

Explanation:

Step1: Recall the properties of dilation

Dilation is a transformation that changes the size of a figure but not its orientation.

Step2: Analyze each option

• For option a: If the dilation is an enlargement, the scale factor is greater than 1. If the rule is \((x,y)\to(2x,2y)\), the scale factor \(k = 2\). For two corresponding segments \(HI\) and \(H'I'\), by the property of dilation \(\frac{H'I'}{HI}=k\).
• For option b: The rule \((x,y)\to(2x,2y)\) means that each coordinate of the original figure is multiplied by 2, which is a valid way to represent a dilation with scale factor \(k = 2\).
• For option c: Dilation only changes the size of the figure. It is a similarity transformation. The orientation (the order of the vertices when going around the figure) remains the same.

Answer:

d. The dilation changed the orientation of the figure.