DILATION

Dilation

Definition Of Dilation

Dilation is a similarity transformation in which a figure is enlarged or reduced using a scale factor ? 0, without altering the center.

More About Dilation

When the scale factor of a dilation is greater than 1, the dilation is an enlargement.
When the scale factor of a dilation is less than 1, the dilation is a reduction.

Example of Dilation

In the figure shown, triangle ADE is enlarged to triangle ABC using a scale factor 4. Here, A is the center of dilation.

example of Dilation

Video Examples: Dilation

Solved Example on Dilation

Ques: A'B'C'D' is a dilation of ABCD. Find the scale factor if AB = 2 × A'B'.

Choices:

A. 2
B. 5
C. 0.5
D. 0.2
Correct Answer: C

Solution:

Step 1: A'B'C'D' is a dilation of ABCD.
Step 2: AB = 2 × A'B' implies A'B' = 0.5 × AB
Step 3: So, the scale factor is 0.5.

Quick Summary

Dilation enlarges or reduces a figure.
Scale factor determines the size change.
If scale factor > 1, it's an enlargement.
If scale factor < 1, it's a reduction.
The center of dilation remains unchanged.

\[ D'(x, y) = (kx, ky), where k is the scale factor \]

🍎 Teacher Insights

Use visual aids and interactive software to demonstrate dilation. Emphasize the relationship between the scale factor and the size change. Provide examples with different centers of dilation.

🎓 Prerequisites

Ratio
Proportion
Similarity

Check Your Knowledge

Q1: A triangle with vertices A(1, 1), B(2, 1), and C(1, 2) is dilated by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the dilated triangle A'B'C'?

A'(3, 3), B'(6, 3), C'(3, 6) A'(1, 1), B'(2, 1), C'(1, 2) A'(4, 4), B'(5, 4), C'(4, 5) A'(0.33, 0.33), B'(0.66, 0.33), C'(0.33, 0.66)

Q2: If AB = 2 × A'B', where A'B' is a dilation of AB, what is the scale factor?

2 5 0.5 0.2

Frequently Asked Questions

Q: What happens if the scale factor is 1?
A: If the scale factor is 1, the figure remains unchanged.

Q: Can the scale factor be negative?
A: While less common in basic geometry, a negative scale factor represents a dilation combined with a rotation of 180 degrees about the center of dilation.