There are three types of ways to move a figure. Let us examine the characteristics of each.
Three Types of Transformations
- Translation: Moving a figure so that only its position changes while its shape, size, and orientation remain the same
- Rotation: Turning a figure by a specified angle around a point (the center); its shape and size do not change
- Reflection (folding over): Using a line as a “mirror” and folding the figure over to the opposite side of the line
Example 1 (Translation): Point A(2, 3) is translated 4 units to the right and 2 units down. Where is the image of the point?
Solution:
① 4 units right → x increases by 4, so 2 + 4 = 6
② 2 units down → y decreases by 2, so 3 − 2 = 1
③ Answer: (6, 1)
Solution:
① 4 units right → x increases by 4, so 2 + 4 = 6
② 2 units down → y decreases by 2, so 3 − 2 = 1
③ Answer: (6, 1)
Example 2 (Reflection): Point B(5, 2) is reflected across the x-axis (the horizontal axis). Where is the image of the point?
Solution: The x-value stays the same, and the sign of the y-value changes → (5, −2)
Solution: The x-value stays the same, and the sign of the y-value changes → (5, −2)
In a rotation, we can construct the image with a compass by using the fact that the distance from the center of rotation does not change.