(8) Inquiry Lab - Dilations

1. WHAT are the results of
a dilation of a triangle?
Course 3, Inquiry Lab before Lesson 6-4
Geometry

2. • 8.G.3
Describe the effect of dilations, translations, rotations, and reflections
on two-dimensional figures using coordinates.
• 8.G.4
Understand that a two-dimensional figure is similar to another if the
second can be obtained from the first by a sequence of rotations,
reflections, translations, and dilations; given two similar two-dimensional
figures, describe a sequence that exhibits the similarity between them.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
5 Use appropriate tools strategically.
Course 3, Inquiry Lab before Lesson 6-4 Common Core State Standards © Copyright 2010. National Governors Association Center for
Best Practices and Council of Chief State School Officers. All rights reserved.
Geometry

3. Course 3, Inquiry Lab before Lesson 6-4
Activity 1
continued

Geometry
In this Activity, you will enlarge by a scale factor of 2 using
grid paper. Point A will be the center point for the enlargement.
ABC
On the grid shown below, is drawn to the edge of the
grid. Draw in the same way.
AB
AC

4. Course 3, Inquiry Lab before Lesson 6-4
Activity 1
continued

Geometry
In this Activity, you will enlarge by a scale factor of 2 using
grid paper. Point A will be the center point for the enlargement.
ABC
Draw point B’ on so that AB’ = 2(AB). Draw point C’ on
So that AC’ = 2(AC).
AB
AC

5. Course 3, Inquiry Lab before Lesson 6-4
Geometry
In this Activity, you will enlarge by a scale factor of 2 using
grid paper. Point A will be the center point for the enlargement.
ABC
Draw to complete .' 'B C ' 'AB C
What is the ratio of the length of to the length of _____________
What is the ratio of the length of to the length of _____________
What is the ratio of the length of to the length of _____________
What do you notice about the ratios of corresponding sides? Is
similar to ___________________________________________
AB 'AB
AC 'AC
BC ' 'B C
ABC
' ' 'A B C

6. Course 3, Inquiry Lab before Lesson 6-4
Activity 2
continued

Geometry
In this Activity, you will draw the image of after a dilation
with a scale factor of . Point C will be the center of dilation.
XYZ
1
2
Triangle XYZ is shown below. Point C is the center of dilation.
Using a ruler, draw line segments connecting C to each of the
vertices of the triangle. is done for youCY

7. Course 3, Inquiry Lab before Lesson 6-4
Activity 2
continued

Geometry
In this Activity, you will draw the image of after a dilation
with a scale factor of . Point C will be the center of dilation.
XYZ
1
2
Measure . Draw point Y’ on so that CY’ = (CY).CY CY
1
2

8. Course 3, Inquiry Lab before Lesson 6-4
Activity 2
continued

Geometry
In this Activity, you will draw the image of after a dilation
with a scale factor of . Point C will be the center of dilation.
XYZ
1
2
Repeat Step 2 for the two remaining sides. Draw point X’ on
so that CX’ = (CX) and point Z’ on so that
CZ’ = (CZ).
CX
1
2
CZ
1
2

9. Course 3, Inquiry Lab before Lesson 6-4
Geometry
In this Activity, you will draw the image of after a dilation
with a scale factor of . Point C will be the center of dilation.
XYZ
1
2
Draw .' ' 'X Y Z
Is the same shape as ?
Measure and compare the corresponding lengths on the original and
new triangles. Describe the relationship between these measurements.
________________________________________________________
________________________________________________________
Measure and compare the corresponding angles on the original and
new triangles. Describe the relationship between these measurements.
________________________________________________________
________________________________________________________
' ' 'X Y Z XYZ

10. Course 3, Inquiry Lab before Lesson 6-4
WHAT are the results of
a dilation of a triangle?
Geometry