Question

which is different? a 90° counterclockwise rotation about the origin a 270° clockwise rotation about the origin a 90° leftward rotation about the origin a 270° counterclockwise rotation about the origin find \both\ answers. answer of the different question: a (□,□), b (□,□), c (□,□) answer of the same three questions: a (□,□), b (□,□), c (□,□)

Explanation:

Step1: Find coordinates of \(A\), \(B\), \(C\)

From the graph, \(A(1,2)\), \(B(2,4)\), \(C(4,2)\)

Step2: Use rotation rules

• For \(90^{\circ}\) counter - clockwise rotation (\(x,y\to -y,x\)):
• \(A(1,2)\to A'(- 2,1)\)
• \(B(2,4)\to B'(-4,2)\)
• \(C(4,2)\to C'(-2,4)\)
• For \(270^{\circ}\) clockwise rotation (\(x,y\to -y,x\)):
• \(A(1,2)\to A'(-2,1)\)
• \(B(2,4)\to B'(-4,2)\)
• \(C(4,2)\to C'(-2,4)\)
• For \(90^{\circ}\) leftward rotation (same as \(90^{\circ}\) counter - clockwise, \(x,y\to -y,x\)):
• \(A(1,2)\to A'(-2,1)\)
• \(B(2,4)\to B'(-4,2)\)
• \(C(4,2)\to C'(-2,4)\)
• For \(270^{\circ}\) counter - clockwise rotation (\(x,y\to y,-x\)):
• \(A(1,2)\to A'(2,-1)\)
• \(B(2,4)\to B'(4,-2)\)
• \(C(4,2)\to C'(2,-4)\)

Answer:

of the different question: \(A'(2,-1)\), \(B'(4,-2)\), \(C'(2,-4)\)