Investigating Scale Factors Adapted from Walch Education Key Concepts The notation is as follows: Dk(x, y) = (kx, ky). • Multiply each coordinate of the figure.
Download ReportTranscript Investigating Scale Factors Adapted from Walch Education Key Concepts The notation is as follows: Dk(x, y) = (kx, ky). • Multiply each coordinate of the figure.
Investigating Scale Factors
Adapted from Walch Education
Key Concepts
The notation is as follows:
D k
(x, y) = (kx, ky).
• Multiply each coordinate of the figure by the scale factor when the center is at (0, 0).
2 1.1.2: Investigating Scale Factors
•
Concepts, continued…
The lengths of each side in a figure also are multiplied by the scale factor.
• If you know the lengths of the preimage figure and the scale factor, you can calculate the lengths of the image by multiplying the preimage lengths by the scale factor.
• The dilation is an enlargement if k > 1, a reduction if 0 < k < 1, and a congruency transformation if k = 1.
3 1.1.2: Investigating Scale Factors
Let’s Practice
A triangle has vertices G (2, –3), H (–6, 2), and J (0, 4). If the triangle is dilated by a scale factor of 0.5 through center C (0, 0), what are the image vertices? Draw the preimage and image on the coordinate plane.
4 1.1.2: Investigating Scale Factors
Step 1
Start with one vertex and multiply each coordinate by the scale factor, k.
D k
= (kx, ky)
G
¢ =
D
0.5
[
G
(2, – 3)] =
D
0.5
(0.5
· 2, 0.5
· – 3) = (1, – 1.5) 5 1.1.2: Investigating Scale Factors
Step 2
Repeat the process with another vertex. Multiply each coordinate of the vertex by the scale factor.
H
¢ =
D
0.5
[
H
( 6, 2)] =
D
0.5
(0.5
· 6, 0.5
· 2) = ( 3,1) 6 1.1.2: Investigating Scale Factors
Step 3
Repeat the process for the last vertex. Multiply each coordinate of the vertex by the scale factor.
J
¢ =
D
0.5
[
J
(0, 4)] =
D
0.5
(0.5
· 0, 0.5
· 4) = (0, 2) 7 1.1.2: Investigating Scale Factors
Step 4
List the image vertices.
G
¢
H
¢ (1, 1.5) ( 3,1)
J
¢ (0, 2) 8 1.1.2: Investigating Scale Factors
Step 5
Draw the preimage and image on the coordinate plane.
9 1.1.2: Investigating Scale Factors
Your turn.
What are the side lengths of with a scale factor of 2.5 given the preimage and image to the right and the information that DE = 1, EF = 9.2, and FD = 8.6?
10 1.1.2: Investigating Scale Factors
Thanks for watching!
Ms. Dambreville