Question

rules for rotation on a coordinate plane
a. $90^{circ}$ rotation clockwise or $270^{circ}$ counterclockwise
$(x,y)\to(y,-x)$
b. $90^{circ}$ rotation counterclockwise or $270^{circ}$ clockwise
$(x,y)\to(-y,x)$
c. $180^{circ}$ rotation
$(x,y)\to(-x,-y)$
d. $360^{circ}$ rotation
$(x,y)\to(x,y)$
quote
a. “to rotate the figure, all x values will be the y values; all y values will be the opposite sign of the x values.”
b. “to rotate the figure, all x values will take the opposite sign; all y values will take the opposite sign.”
c. “to rotate the figure, all x values will take the opposite sign of the y values; the x values will take the y values; all y values will take the x values.”
d. “to rotate the figure, all x values will remain the same; all y values will remain the same.”

Explanation:

Step1: Analyze 90° clockwise or 270° counter - clockwise rotation

For a point \((x,y)\) rotated 90° clockwise or 270° counter - clockwise, the new coordinates are \((y, - x)\).

Step2: Analyze 90° counter - clockwise or 270° clockwise rotation

For a point \((x,y)\) rotated 90° counter - clockwise or 270° clockwise, the new coordinates are \((-y,x)\).

Step3: Analyze 180° rotation

For a point \((x,y)\) rotated 180°, the new coordinates are \((-x,-y)\).

Step4: Analyze 360° rotation

For a point \((x,y)\) rotated 360°, the new coordinates are \((x,y)\) (all \(x\) values remain the same; all \(y\) values remain the same).

Answer:

A. \((x,y)\to(y, - x)\)
B. \((x,y)\to(-y,x)\)
C. \((x,y)\to(-x,-y)\)
D. \((x,y)\to(x,y)\)