Question

the diagram shows ( r_{(90^{circ},o)}(abcd) ). what are the coordinates of abcd?
a (type your answer as an ordered pair in parentheses)
b
c
d

Explanation:

Step1: Recall the rotation rule

The rotation \(r_{(90^{\circ},O)}\) (counter - clockwise rotation about the origin by \(90^{\circ}\)) has the rule \((x,y)\to(-y,x)\).

Step2: Find the coordinates of \(A'\), \(B'\), \(C'\), \(D'\)

From the graph: \(A'(-1,1)\), \(B'(-5, - 1)\), \(C'(-3,-7)\), \(D'(-1,-3)\)

Step3: Apply the inverse rotation rule

Since \(r_{(90^{\circ},O)}(ABCD)=A'B'C'D'\), to get \(ABCD\) from \(A'B'C'D'\), we use the inverse rotation (clockwise rotation about the origin by \(90^{\circ}\)) rule \((x,y)\to(y, - x)\)

• For \(A'(-1,1)\): \(A(1,1)\)
• For \(B'(-5,-1)\): \(B(-1,5)\)
• For \(C'(-3,-7)\): \(C(-7,3)\)
• For \(D'(-1,-3)\): \(D(-3,1)\)

Answer:

A\((1,1)\)
B\((-1,5)\)
C\((-7,3)\)
D\((-3,1)\)