Question

1. discussion question: compare the (x,y) coordinate points from the pre - image to the image for all reflections over the line y = x. find a pattern. what pattern did you find? _______________

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will this work for all reflections over any line? yes/no (circle one).

1. reflect the quadrilateral over the line x = - 2. p(-4,4), q(0,6), r(3,-1), s(-1,2)

Explanation:

Step1: Analyze reflection over y = x

When reflecting a point (x,y) over the line y = x, the x - coordinate and y - coordinate swap. So the pattern is that if the pre - image is (x,y), the image is (y,x).

Step2: Determine if it works for all lines

No, this pattern only works for reflection over the line y = x. For other lines of reflection, different transformation rules apply.

Step3: Reflect points over x = - 2

The formula for reflecting a point (x,y) over the vertical line x = a is (2a - x,y). Here a=-2.
For point P(-4,4):
2(-2)-(-4)=-4 + 4=0, so P'=(0,4)
For point Q(0,6):
2(-2)-0=-4, so Q'=(-4,6)
For point R(3,-1):
2(-2)-3=-4 - 3=-7, so R'=(-7,-1)
For point S(-1,2):
2(-2)-(-1)=-4 + 1=-3, so S'=(-3,2)

Answer:

What pattern did you find? The x and y coordinates swap.
Will this work for ALL reflections over any line? NO
P'(0,4)
Q'(-4,6)
R'(-7,-1)
S'(-3,2)