Question

after a rotation, a(-3, 4) maps to a(4, 3), b(4, -5) maps to b(-5, -4), and c(1, 0) maps to c(0, -1). which rule describes the rotation?
r0, 90°
r0, 180°
r0, 270°
r0, 360°

Explanation:

Step1: Recall rotation rules

For a 90 - degree counter - clockwise rotation about the origin $(x,y)\to(-y,x)$. For a 180 - degree rotation about the origin $(x,y)\to(-x,-y)$. For a 270 - degree counter - clockwise rotation about the origin $(x,y)\to(y, - x)$. For a 360 - degree rotation about the origin $(x,y)\to(x,y)$.

Step2: Analyze point A

Given $A(-3,4)$ maps to $A'(4,3)$. If we consider the 90 - degree counter - clockwise rotation rule: for $A(-3,4)$, applying $(x,y)\to(-y,x)$ gives $(-4,-3)$ which is wrong. For 180 - degree rotation, for $A(-3,4)$ applying $(x,y)\to(-x,-y)$ gives $(3,-4)$ which is wrong. For 270 - degree counter - clockwise rotation, for $A(-3,4)$ applying $(x,y)\to(y,-x)$ gives $(4,3)$ which is correct.

Step3: Check other points

For $B(4,-5)$, applying 270 - degree counter - clockwise rotation $(x,y)\to(y,-x)$ gives $(-5,-4)$ which is $B'$. For $C(1,0)$, applying 270 - degree counter - clockwise rotation $(x,y)\to(y,-x)$ gives $(0,-1)$ which is $C'$.

Answer:

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