Answer: You'll have a quadrilateral with the following points
- (5, -5)
- (4, -7)
- (6, -7)
- (8, -3)
A diagram is posted below.
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Explanation:
The given quadrilateral has four unmarked points. I'll add the point labels A,B,C,D such that
- A = (-3, 3)
- B = (-5, 2)
- C = (-5, 4)
- D = (-1, 6)
I started at the lower right corner and worked my way clockwise.
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Let's shift the line y = x-2 up two units so that it moves to y = x
We'll need to shift every point of the quadrilateral up two units as well.
So we have these new point locations after the shifting has occurred.
- A' = (-3, 5)
- B' = (-5, 4)
- C' = (-5, 6)
- D' = (-1, 8)
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Now we need to reflect over the diagonal line. The rule to reflect over the line y = x is as simple as swapping the x and y coordinates.
So we can say [tex](x,y) \to (y,x)[/tex]
A point like (-3, 5) moves to (5, -3)
We have these new locations
- A'' = (5, -3)
- B'' = (4, -5)
- C'' = (6, -5)
- D'' = (8, -1)
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The last thing to do is to shift everything down 2 units. This is to undo the first step we did when we shifted everything up by 2 units.
Doing this leads to these locations
- A''' = (5, -5)
- B''' = (4, -7)
- C''' = (6, -7)
- D''' = (8, -3)
Check out the diagram below.
