Use the same interactive sketch to complete the following table. Reset the sketch and make sure that the “Show distances” check box is selected. Move the center of dilation, Point O, outside of rectangle ABCD.

For example, you could move Point O above and to the right of Point B.

screen shot of the interactive sketch with Point O moved above and to the right of Point B

Make a copy of the table, and paste it into your notes. Fill in the columns for Length of OB and Length of OB'. Use the slider to adjust the scale factor while you keep the length of OB the same.

Length of OB	Scale Factor	Length of OB'
	0.5
	0.7
	1.3
	1.4
	1.8
	2

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Check Your Answer

Use the data in your table to answer the questions that follow.

How does the length of OB' compare to the length of OB and the scale factor?
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Check Your Answer
The length of OB' is equal to the product of the length of OB and the scale factor.
Does the location of the center of dilation, with respect to the polygon being dilated, change the relationship you observed before between the scale factor and the distance between a point in a polygon and the center of dilation?
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Check Your Answer
No, the location of the center of dilation does not seem to change the relationship.
Change the shape of quadrilateral ABCD by clicking and dragging Point B to move it. Is the relationship you just observed true for other polygons as well?
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Check Your Answer
Yes. Regardless of the shape of the polygon, the distance from the center of dilation to the dilated point on the polygon is the product of the scale factor and the distance from the center of dilation to the original point.
Click and move the slider to change the scale factor. How does the location of Point C' compare to ray OC, created by starting with Point O and extending a part of a line through Point C?
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Check Your Answer
Point C' appears to move along ray OC as the scale factor changes.

Practice

A trapezoid has coordinates at P (−4, 3), Q (5, 3), R (6, −2), and S (−6, −2). It is dilated by a scale factor of 1.5 with (0, 0) as the center of dilation.

Triangle S T U graphed on a coordinate plane

What are the coordinates of each vertex after the dilation is performed?
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Click for a hint
The dilation has a scale factor of 1.5, which is greater than 1, so it will be an enlargement. The coordinates of the dilated triangle should all be farther from the origin.
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Check Your Answer
P' (−6, 4.5), Q' (7.5, 4.5), R' (9, −3), S' (−9, −3)
Suppose Trapezoid PQRS were dilated by a scale factor of 3 over 5 3 5 with the origin as the center of dilation. What would be the coordinates of each vertex of trapezoid P'Q'R'S'?
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Click for a hint
The dilation has a scale factor of 3 5 , which is less than 1, so it will be a reduction. The coordinates of the dilated triangle should all be closer to the origin.
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Check Your Answer
Suppose Trapezoid PQRS were dilated by scale factor k to generate an enlargement. Which of the following points could be the coordinates of Q'?

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Click for a hint
The points will only be coordinates of Q' if they lie on the ray connecting the origin with Point Q and are outside of the trapezoid, since the dilation is an enlargement.
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Check Your Answer