What set of reflections would carry rectangle abcd onto itself
Asked by maham237 @ in Mathematics viewed by 348 People
y-axis, x-axis, y-axis, x-axis
x-axis, y=x, y-axis, x-axis
x-axis, y-axis, x-axis
y=x, axis, x-axis
Answered by maham237 @
- Reflection about the y-axis has rule (x,y)→(-x,y);
- Reflection about the x-axis has rule: (x,y)→(x,-y).
Consider rectangle ABCD and select, for example point A(-5,1).The set of reflections about the y-axis, x-axis, y-axis, x-axis will act on A in following way:
- about y-axis A(-5,1)→A'(5,1);
- about x-axis A'(5,1)→A''(5,-1);
- about y-axis A''(5,-1)→A'''(-5,-1);
- about x-axis A'''(-5,-1)→A(-5,1).
This reflections act on all rectangle vertices in the same way, then
the set of reflections that carry rectangle ABCD onto itself is
y-axis, x-axis, y-axis, x-axis
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