m (x,y) --> (-x,y) is what transformation reflection rotation or translation
m (x,y) --> (y, -x) is what transformation reflection rotation or translation
m (x,y) --> (2x,2y) is what transformation reflection rotation or translation
how do you do this what are some good videos to watch?
reflection through the y-axis
reflection through the line y = -x
scaling by a factor of 2
a simple web search will provide many references and videos on the topic.
To determine the type of transformation for each given mapping, we can analyze the changes in the coordinates. Here's how you can approach it:
1. For the first mapping: m(x, y) → (-x, y)
Here, the x-coordinate is negated, and the y-coordinate remains the same. This type of transformation is called a reflection because it reflects the figure across the y-axis.
2. For the second mapping: m(x, y) → (y, -x)
In this case, the x-coordinate is replaced with the negated y-coordinate, and the y-coordinate is replaced with the negated x-coordinate. This transformation is a rotation of 90 degrees counterclockwise around the origin.
3. For the third mapping: m(x, y) → (2x, 2y)
In this situation, both the x-coordinate and the y-coordinate are doubled. This type of transformation is known as a dilation or enlargement. The figure is scaled by a factor of 2 in both dimensions.
To better understand these transformations, you can search for videos on platforms like YouTube. Here are some video recommendations to help you grasp the concepts:
- Khan Academy: They provide comprehensive tutorials on geometry and transformations. Visit their YouTube channel and search for "transformations" to find relevant videos.
- Math Antics: They offer engaging math lessons and have videos specifically dedicated to transformations. Search for "Math Antics transformations" on YouTube.
- Math Is Fun: This website has interactive lessons on transformations and provides clear explanations with examples. You can visit their website and search for "transformations videos" to access their video content.
Watching these videos will provide visual demonstrations and explanations, making it easier to understand the different types of transformations.