SME
Grade 10 Math · Problem type
Which motion is the rule?
Use this for “Is (x, y) → (2x, 2y) a rigid motion? Which move is (x, y) → (−y, x)?”
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Which motion does the rule make?
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Assumptions
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A rigid motion keeps every length and every angle.
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Adding to x or y slides; changing one sign, or swapping x and y, flips; (−y, x) and (−x, −y) turn.
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Multiplying a coordinate by a number other than 1 or −1 stretches: not rigid.
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Related lessons
Rigid motions, compositions and symmetry
Main lesson
A glide reflection
Use this for “Translate A(1, 2) 5 units right, then reflect it across the x-axis.”
Rotating about a point
Use this for “Rotate A(6, 2) 90° counterclockwise about the point (1, 1).”
Reflecting across y = x or y = −x
Use this for “Reflect A(4, 1) across the line y = x” or “across y = −x.”
Symmetry of a rectangle
Use this for “Which rotations carry a 6 by 4 rectangle onto itself? How many lines of symmetry does it have?”