Math Plane Figure Geometry

Prove that ΔABC is congruent to ΔDEF with the given vertices.

• The triangles are congruent because ΔABC can be mapped onto ΔDEF by a rotation: (x, y) à (y, − x), followed by a reflection: (x, y) à (x, −y). 

• The triangles are congruent because ΔABC can be mapped onto ΔDEF by a reflection: (x, y) à (-x, y), followed by a rotation: (x, y) à (y, −x). 

• The triangles are congruent because ΔABC can be mapped onto ΔDEF by a translation: (x, y) à (x – 4, y), followed by another translation: (x, y) à (x, y – 6). 

• The triangles are congruent because ΔABC can be mapped onto ΔDEF by a rotation: (x, y) à (−y, x), followed by a reflection: (x, y) à (x, −y). 

Tags

MA.912.GR.2.3

Which sequence of transformations maps ΔABC onto ΔDEF?

• A reflection over the x−axis followed by a reflection over the y−axis 

• A 180° rotation about the origin followed by a reflection over the line y = x 

• A 90° clockwise rotation about the origin followed by a reflection over the y−axis 

• A translation 8 units to the right and 1 unit up followed by a 90° counterclockwise rotation about the origin 

Tags

MA.912.GR.2.3

Figure 1 is reflected about the x−axis and then translated four units left. Which figure results? 

• Figure A 

• Figure B 

• Figure C 

• Figure D 

Tags

MA.912.GR.2.5

Which congruence transformations map ΔXYZ to ΔX’’Y’’Z’’? Select all that apply.

• reflection in the y-axis, followed by a reflection in the x-axis 

• rotation of 90° counterclockwise about the origin, followed by a reflection in the y-axis 

• rotation of 270° counterclockwise about the origin, followed by a reflection in the x-axis 

• reflection in the x-axis, followed by a reflection in the y-axis 

• reflection in the x-axis, followed by a rotation of 90° counterclockwise about the origin 

Tags

MA.912.GR.2.6

A reflection over the x−axis maps ΔABC to ΔA′B′C′.  

Do the preimage and image have the same size and shape? Explain. 

Choose the correct answer below. 

• No. A reflection preserves only lengths of sides. 

• Yes. A reflection preserves both angle measures and lengths of sides. 

• No. A reflection preserves neither angle measures nor lengths of sides. 

• No. A reflection preserves only angle measures. 

Tags

MA.912.GR.2.2

MA.912.GR.2.6

Quadrilateral ABCD has vertices A(−1,3), B(−1,7), C(−5,7), and D(−5,3) . Vertex B is translated 4 units up and the other vertices do not change position. How much larger is the area of quadrilateral AB'CD than the area of quadrilateral ABCD ? 

• 3 times larger

• 2.5 times larger 

• 2 times larger 

• 1.5 times larger 

Tags

MA.912.GR.2.2

ΔXYZ with vertices X(4, 8), Y(12, 14), and Z(8, 12) is dilated by a scale factor of 0.25 and then is rotated 90° clockwise about the origin. Determine which quadrant the image is located in without performing the transformations 

• Quadrant I

• Quadrant II 

• Quadrant III 

• Quadrant IV 

Tags

MA.912.GR.2.3

Tags

MA.912.GR.2.3

Determine whether the octagon has rotational symmetry. If so, identify the order of rotational symmetry.

• The octagon has rotational symmetry. The order of rotational symmetry is 2. 

• The octagon has rotational symmetry. The order of rotational symmetry is 4. 

• The octagon has rotational symmetry. The order of rotational symmetry is 8. 

• The octagon does not have rotational symmetry 

Tags

MA.912.GR.2.4

The vertices of ΔABC are A (–4, 5), B (–2, 4) and C (–3, 3).  ΔABC is reflected across the y−axis, then reflected across the x−axis to produce the image ΔA’B’C’. Which graph shows the pre−image and image of the transformation? 

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Tags

MA.912.GR.2.5