Triangle ABC is transformed to create triangle DEF. What sequence of transformations maps one to the other? Select all that apply.
A.Rotate 180° about the origin, then translate left 2 units
B.Reflect over the x-axis, then translate down 2 units
C.Translate 2 units to the right, then rotate 180° about the origin
D.Translate 2 units to the right, then reflect over the x-axis
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To determine the sequence of transformations that maps triangle ABC to triangle DEF, we need to analyze the given options.
A. Rotate 180° about the origin, then translate left 2 units:
This transformation alone rotates the triangle 180° but does not move it left or right. Therefore, option A will not create triangle DEF.
B. Reflect over the x-axis, then translate down 2 units:
This sequence first reflects the triangle over the x-axis and then moves it down 2 units. Both of these transformations change the position of the triangle, so option B is a valid sequence of transformations.
C. Translate 2 units to the right, then rotate 180° about the origin:
This sequence firstly translates the triangle 2 units to the right, then rotates it 180° about the origin. These transformations both move and rotate the triangle, so option C is a valid sequence of transformations.
D. Translate 2 units to the right, then reflect over the x-axis:
This sequence first translates the triangle 2 units to the right and then reflects it over the x-axis. These transformations both change the position and orientation of the triangle, so option D is a valid sequence of transformations.
Therefore, the correct answers are B, C, and D.
To determine the sequence of transformations that maps one triangle to another, we need to examine the properties of each transformation and how they affect the position and orientation of the triangle.
A.Rotate 180° about the origin, then translate left 2 units:
This transformation rotates the triangle 180 degrees around the origin (a point where x and y coordinates are zero) and then moves it 2 units to the left. This is a valid transformation but does not necessarily map triangle ABC to triangle DEF.
B.Reflect over the x-axis, then translate down 2 units:
This transformation reflects the triangle over the x-axis (where the y-coordinate changes its sign) and then moves it 2 units downward. This is a valid transformation and can potentially map triangle ABC to triangle DEF, as it changes the orientation and position of the triangle.
C.Translate 2 units to the right, then rotate 180° about the origin:
This transformation first moves the triangle 2 units to the right and then rotates it 180 degrees around the origin. While this sequence of transformations changes the position and orientation of the triangle, it does not necessarily map triangle ABC to triangle DEF.
D.Translate 2 units to the right, then reflect over the x-axis:
This transformation first moves the triangle 2 units to the right and then reflects it over the x-axis. This is a valid transformation and can potentially map triangle ABC to triangle DEF, as it changes the position and orientation of the triangle.
Therefore, the sequences of transformations that can map triangle ABC to triangle DEF are options B and D:
B.Reflect over the x-axis, then translate down 2 units.
D.Translate 2 units to the right, then reflect over the x-axis.
no picture.
Confused? Cut out a triangle and try the transformations to see which works.