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6.03 Rotations

Adaptive
Worksheet

Interactive practice questions

What is the correct image after $M$M is rotated $180^\circ$180° clockwise about the origin?

On a Coordinate Plane, four identical triangles that share a common vertex at the origin $\left(0,0\right)$(0,0) are plotted. In every quadrant there is one triangle.  The triangle in the first quadrant is shaded green and is labeled as triangle $Q$Q. The triangle in the second quadrant is shaded blue and is labeled as triangle $P$P. The triangle in the third quadrant is shaded orange and is labeled as triangle $N$N. The triangle in the fourth quadrant is shaded purple and is labeled as triangle $M$M. The triangles are arranged like a pinwheel where each subsequent triangle is a $90^\circ$90° rotation of the previous one. In clockwise rotation, triangle $M$M is subsequent to triangle $Q$Q, triangle $N$N is subsequent to triangle $M$M, triangle $P$P is subsequent to triangle $N$N, and triangle $Q$Q is subsequent to triangle $P$P.

$N$N

A

$Q$Q

B

$P$P

C
Easy
< 1min

Which of these is a rotation of shape $M$M by $90^\circ$90° counterclockwise about the origin?

Easy
< 1min

What is the correct image after $Q$Q is rotated $90^\circ$90° counterclockwise about the origin?

Easy
< 1min

Which of these is a rotation of shape $E$E by $270^\circ$270° clockwise about the origin?

Easy
< 1min
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Outcomes

M2.G.CO.A.1

Describe transformations as functions that take points in the plane (pre-image) as inputs and give other points (image) as outputs. Compare transformations that preserve distance and angle measure to those that do not, by hand for basic transformations and using technology for more complex cases.

M2.G.CO.A.2

Given a rectangle, parallelogram, trapezoid, or regular polygon, determine the transformations that carry the shape onto itself and describe them in terms of the symmetry of the figure.

M2.G.CO.A.3

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

M2.G.CO.A.4

Given a geometric figure, draw the image of the figure after a sequence of one or more rigid motions, by hand and using technology. Identify a sequence of rigid motions that will carry a given figure onto another.

M2.MP1

Make sense of problems and persevere in solving them.

M2.MP2

Reason abstractly and quantitatively.

M2.MP3

Construct viable arguments and critique the reasoning of others.

M2.MP5

Use appropriate tools strategically.

M2.MP6

Attend to precision.

M2.MP7

Look for and make use of structure.

M2.MP8

Look for and express regularity in repeated reasoning.

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