Question

the graph of \\( \triangle abc \\) is shown
which is different?
\\( \bigcirc \\) a \\( 90^{\circ} \\) counterclockwise rotation about the origin
\\( \bigcirc \\) a \\( 270^{\circ} \\) clockwise rotation about the origin
\\( \bigcirc \\) a \\( 90^{\circ} \\) leftward rotation about the origin
\\( \bigcirc \\) a \\( 270^{\circ} \\) counterclockwise rotation about the origin
find \both\ answers.
answer of the different question: \\( a(\square \square), b(\square \square), c(\square \square) \\)
answer of the same three questions: \\( a(\square \square), b(\square \square), c(\square \square) \\)

Explanation:

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

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

Step2: Apply rotation rules

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

Answer:

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