Question

after a rotation, a(-3, 4) maps to a(4, 3), b(4, -5) maps to b(-5, -4), and c(1, 6) maps to c(6, -1). which rule describes the rotation?
$r_{0, 90^{circ}}$
$r_{0, 180^{circ}}$
$r_{0, 270^{circ}}$
$r_{0, 360^{circ}}$

Explanation:

Step1: Recall rotation rules

The general rules for rotation about the origin $(0,0)$ are:

• $R_{0,90^{\circ}}(x,y)=(-y,x)$
• $R_{0,180^{\circ}}(x,y)=(-x,-y)$
• $R_{0,270^{\circ}}(x,y)=(y, - x)$
• $R_{0,360^{\circ}}(x,y)=(x,y)$

Step2: Test the rule for point A

For point $A(-3,4)$, if we apply $R_{0,270^{\circ}}$:
$R_{0,270^{\circ}}(-3,4)=(4,-(-3))=(4,3)$ which is $A'$.

Step3: Test the rule for point B

For point $B(4, - 5)$, if we apply $R_{0,270^{\circ}}$:
$R_{0,270^{\circ}}(4,-5)=(-5,-4)$ which is $B'$.

Step4: Test the rule for point C

For point $C(1,6)$, if we apply $R_{0,270^{\circ}}$:
$R_{0,270^{\circ}}(1,6)=(6,-1)$ which is $C'$.

Answer:

$R_{0,270^{\circ}}$