Question

which of the following is not a true statement about the dilation shown?
the ratio of \\( \frac { h ^ { prime } i ^ { prime } } { h i } = \frac { i ^ { prime } j ^ { prime } } { i j } \\)
the dilation can be represented by \\( ( x, y ) \
ightarrow ( 2 x, 2 y ) \\)
the dilation represents an enlargement.
the dilation changed the orientation of the figure.
clear my selection

Explanation:

Step1: Analyze the dilation properties

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

Step2: Check each option

• For the ratio \(\frac{H'I'}{HI}=\frac{I'J'}{IJ}\), in dilation, corresponding side lengths are proportional.
• For the dilation \((x,y)\to(2x,2y)\), if we take a point \(H(- 2,2)\) and \(H'(-4,4)\), \(x=-2\to - 4 = 2\times(-2)\), \(y = 2\to4=2\times2\).
• Since the image \(H'I'J'K'\) is larger than \(HIJK\), it is an enlargement.
• Dilation does not change the orientation of the figure.

Answer:

The dilation changed the orientation of the figure.