Question

△abc is translated 2 units down and 1 unit to the left. then it is rotated 90° clockwise about the origin to form △abc
the coordinates of vertex a of △abc are
the coordinates of vertex b of △abc are
the coordinates of vertex c of △abc are

Explanation:

Step1: Find coordinates after translation

• Original coordinates: \(A(0,0)\), \(B(1,3)\), \(C(1,1)\)
• Translation rule: \((x,y)\to(x - 1,y - 2)\)
• After translation: \(A_1(-1,-2)\), \(B_1(0,1)\), \(C_1(0,-1)\)

Step2: Apply \(90^{\circ}\) clockwise rotation

• Rotation rule: \((x,y)\to(y,-x)\)
• For \(A_1(-1,-2)\): \(A'(-2, -1)\)
• For \(B_1(0,1)\): \(B'(1, -2)\)
• For \(C_1(0,-1)\): \(C'(2, -1)\)

Answer:

• Coordinates of \(A'\): \((-2, -1)\)
• Coordinates of \(B'\): \((1, -2)\)
• Coordinates of \(C'\): \((2, -1)\)