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what set of transformations could be applied to rectangle ABCD to create A’B’C’D’?

A)Reflected over the x-axis and rotated 180 degrees

B)Reflected over the y-axis and rotated 180 degrees

C)Reflected over the x-axis and rotated 90 degrees counterclockwise

D)Reflected over the y-axis and rotated 90 degrees counterclockwise

what set of transformations could be applied to rectangle ABCD to create ABCD AReflected over the xaxis and rotated 180 degrees BReflected over the yaxis and ro class=

Respuesta :

frika

Rectangle ABCD has vertices A(-4,2), B(-4,1), C(-1,1) and D(-1,2).

1. Apply the reflection over the x-axis that has a rule

(x,y)→(x,-y).

Then

  • A(-4,2)→A''(-4,-2);
  • B(-4,1)→B''(-4,-1);
  • C(-1,1)→C''(-1,-1);
  • D(-1,2)→D''(-1,-2).

2. The second transformation is rotation by 90° counterclockwise about the origin. This transformation has a rule

(x,y)→(-y,x).

Then

  • A''(-4,-2)→A'(2,-4);
  • B''(-4,-1)→B'(1,-4);
  • C''(-1,-1)→C'(1,-1);
  • D''(-1,-2)→D'(2,-1).

As you can see these points are exactly those frome the diagram.

Answer: 1st transformation is reflection over the x-axis and second transformation is rotation by 90° counterclockwise about the origin.

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