Rotations: Practice

A rotation uses one center, one angle, and one direction for the whole plane. Each off-center point stays at its own radius, and the center stays fixed.

A rotation keeps a point at the same distance from its center.

$OJ'=OJ$

Thus $OJ'=4.6$ cm. The 55 degrees describes the turn, not a length.

The center has radius zero and maps to itself. Every other point turns 73 degrees around a positive-radius circle, so it moves.

A negative sign chooses clockwise direction. The magnitude gives the amount of turning.

$|-270|=270$

The instruction is 270 degrees clockwise. Its final image also agrees with a 90-degree counterclockwise turn, but the stated motion is longer.

Use the counterclockwise quarter-turn rule $(x,y)\mapsto(-y,x)$.

$(-4,6)\mapsto(-6,-4)$

A half-turn reverses both coordinate directions. Negate both coordinates.

$(7,-1)\mapsto(-7,1)$

Use the clockwise quarter-turn rule $(x,y)\mapsto(y,-x)$.

$(-3,-5)\mapsto(-5,3)$

A 270-degree clockwise turn reaches the same final ray as a 90-degree counterclockwise turn. Use $(-y,x)$.

$(1,-6)\mapsto(6,1)$

A rotation preserves distance and angle measure directly. The image segment remains 10 cm long, and the corresponding image angle remains 38 degrees.

A rotation turns the marked face without flipping it. It preserves the clockwise or counterclockwise order of corresponding triangle vertices, whichever direction the figure itself turns.

A full turn returns every point to its starting ray at its original radius.

$P'=P$

This is an identity rotation; every point is fixed.

The angle and direction have already chosen the new ray. The remaining rotation condition is the unchanged radius, so copy length OP from O along that ray.