Unit 8 Lesson 4: Dilating Figures

Question 1

center of dilation

Answer 1

the point of reference used as the foundation for a dilation on the coordinate plane

Question 2

dilation

Answer 2

the act or process of expanding or reducing a shape by the same scale factor

Question 3

magnitude

Answer 3

the size of an object or image; scale factor

Question 4

scale factor

Answer 4

a number representing the ratio between the dimension of an object and the dimension of a dilation of that object

Question 5

. A more accurate way to think about the center of dilation is that all dilations center on that particular point. elaborate

Answer 5

If the dilation is 3 and point x
is being transformed into point x’
, then point x’
will be three times further from point x
than point x
is from the center of dilation. Similarly, if the dilation is 12
and point y
is being transformed into point y’
, point y’
will be halfway between point y
and the center of dilation.

Question 6

Darian uses a scale factor of 4 to dilate a pentagon on the coordinate plane with the origin as the center of dilation. Will the dilated pentagon be larger or smaller than the original? How do you know?

Answer 6

It will be larger. Darian is using a scale factor that is greater than 1, so the coordinates will all increase relative to the origin.

Question 7

Fiona dilates a square on the coordinate plane using the origin as the center of dilation. If the dilated square is smaller than the original, what must be true?

Answer 7

The scale factor must be less than 1 and greater than 0.

Question 8

Jane draws a triangle on the coordinate plane and then dilates it using the origin as the center of dilation. The scale factor of the dilation is 1.5 and one of the vertices of the original triangle is at point (9,8)
. What are the coordinates of the corresponding vertex in the dilated triangle?

Answer 8

The coordinates of the corresponding vertex are (13.5,12)
.