1. Similarity and Transformations
7-2
Similarity and Transformations
Holt Geometry
Holt McDougal Geometry

2. Warm Up
Find the image point when the indicated transformation is applied to the given pre-image point.
1. (x, y) → (x + 3, y – 1); (2, 4)
2. (x, y) → (x, –y); (–2, 1)
3. (x, y) → (3x, 3y); (–5, 0) 3 1 x, y
4. (x, y) →
; (3, -6)

3. A transformation that produces similar figures is a similarity transformation.
A similarity transformation is a dilation or a composite of one or more dilations and one or more congruence transformations.
Two figures are similar if and only if there is a similarity transformation that maps one figure to the other figure.
The scale factor describes how the figure is enlarged or reduced.

4. Translations, reflections, and rotations are congruence transformations.
Dilations are similarity transformations.
Remember!

5. A. Apply the dilation D to the polygon with the given vertices
A. Apply the dilation D to the polygon with the given vertices. Describe the dilation.
D: (x, y) → (3x, 3y) A(1, 1), B(3, 1), C(3, 2)

6. Apply the dilation D : (x, y)→
polygon with vertices D(-8, 0), E(-8, -4), and F(-4, -8). Name the coordinates of the image points. Describe the dilation.
to the 4 1 x, y

7. Determine whether the polygons with the given vertices are similar
Determine whether the polygons with the given vertices are similar. If so, give the rule.
A. A(–6, -6), B(-6, 3), C(3, 3),
D(3, -6) and H(-2, -2),
J(-2, 1), K(1, 1), L(1, -2)

8. B. P(2, 0), Q(2, 4), R(4, 4),
S(4, 0) and W(5, 0),
X(5, 10), Y(8, 10), Z(8, 0).

10. A. Circle A with center (0, 0) and radius 1 is similar to circle B with center (0, 6) and radius 3.

11. B. Circle C with center (0, –3) and radius 2 is similar to circle D with center (5, 1) and radius 5.

12. Prove that circle A with center (2, 1) and radius 4 is similar to circle B with center (-1, -1) and radius 2.

13. Explore dilations further
Record observations using a scale factor of 2
Characteristics
Original Circle with diameter AB
New circle with diameter A’B’
Observations
Coordinates
A(4,1) B(4,-3)
Length of diameter
4 cm
Length of radius
Circumference
Area

14. 1. Apply the dilation D: (x, y)
to the
polygon with vertices A(2, 4), B(2, 6), and C(6, 4). Name the coordinates of the image points. Describe the dilation.

15. Determine whether the polygons with the given vertices are similar.
2. A(-4, 4), B(6, 4), C(6, -4),
D(-4, -4) and P(-2, 2),
Q(4, 2), R(4, -2), S(-2, -2)

16. 3. Prove that circle A with center (0, 4) and radius 4 is similar to circle B with center (-2, -7) and radius 6.

17. Homework