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What set of reflections would carry rectangle ABCD onto itself?




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

What set of reflections would carry rectangle ABCD onto itself? 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-a class=

Verified Answer :

Hagrid

The set of reflections that would carry rectangle ABCD back to itself is:
y-axis, x-axis, y-axis, x-axis.

By reflecting the original image over y-axis, the transformed image moves to the 1st quadrant of the cartesian plane. By reflecting the image in quadtrant 1 over x-axis, the image moves to the 4th quadrant, and by reflecting it again over y-axis and another over the x-axis, it goes back to its original position in the 2nd quadrant.

frika

  • 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:

  1. about y-axis A(-5,1)→A'(5,1);
  2. about x-axis A'(5,1)→A''(5,-1);
  3. about y-axis A''(5,-1)→A'''(-5,-1);
  4. 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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