We did graphing reflections of images homework from the book with problems that gave the vertices for each figure and said either reflect over x or y. This time, the homework is a worksheet and directions are to graph the reflection across either x or y with some value.
Example problem:
Graph the image of the figure using the transformation given.
1. reflection across y = -2. (Also, the figure is given, but need to figure out the coordinates).
original image: I(-3, -2), E(-3, -3), Q(2, -4), Z(0,-5)
a. Can you explain what does the across y = -2 mean? I know if we reflect over y, then the x value is multiplied by -1 and y stays the same. Am i supposed to multiply the x coordinate by -2? If i know how to solve, then i can do 4 others with different y value.
2. reflection across y = -x. (orignal image is A(3, -1), J(4, -3), S(4,2), T(5, -2)
a. Can you explain what does across y= -x mean?
3. reflect across y = x (original image H(-2, -3), L(0,3), Q(-2, -1), P (-3, -2)
a. Can you explain what does across y= x mean?
To understand the directions "reflection across y = -2" or "reflection across y = -x" or "reflection across y = x," it's important to recall the basic concept of reflecting a point across a line.
When reflecting a point across the y-axis, every point (x, y) is transformed to (-x, y). This means that the x-coordinate is multiplied by -1 while the y-coordinate remains the same.
Let's break down the example problems to understand each direction in more detail:
1. reflection across y = -2:
To reflect the original image (I(-3, -2), E(-3, -3), Q(2, -4), Z(0, -5)) across the line y = -2, you need to keep the y-coordinate the same and change the x-coordinate accordingly.
For example, let's take the point I(-3, -2). To reflect it across y = -2, you would substitute -2 as the y-coordinate and adjust the x-coordinate. Thus, the reflected point would be I(3, -2).
Apply the same process to each point and replace the x-coordinate accordingly. The reflected image would be I'(3, -2), E'(-3, -3), Q'(2, -4), Z'(0, -5).
2. reflection across y = -x:
When reflecting across y = -x, each point (x, y) is transformed to (-y, -x). Here, the y-coordinate becomes the negative of the original x-coordinate, and the negative of the original y-coordinate becomes the new x-coordinate.
Consider the original image A(3, -1), J(4, -3), S(4, 2), T(5, -2). To reflect it across y = -x, substitute the coordinates accordingly.
For instance, A(3, -1) would transform to A'(-1, -3), J(4, -3) would transform to J'(-3, -4), S(4, 2) would transform to S'(-2, -4), and T(5, -2) would transform to T'(-2, -5).
3. reflection across y = x:
Similar to the previous explanations, when reflecting across y = x, each point (x, y) becomes (y, x). The x-coordinate becomes the new y-coordinate, and the y-coordinate becomes the new x-coordinate.
Considering the original image H(-2, -3), L(0, 3), Q(-2, -1), P(-3, -2), to reflect it across y = x, substitute the coordinates accordingly.
For instance, H(-2, -3) would transform to H'(-3, -2), L(0, 3) would transform to L'(3, 0), Q(-2, -1) would transform to Q'(-1, -2), and P(-3, -2) would transform to P'(-2, -3).
By following these steps and understanding the rules of reflecting points across a given line, you'll be able to solve other problems on the worksheet with different y-values.