Question

23
triangle abc has vertices a (1, -3), b (3, -2) and c (0, -1). rotate triangle abc 90 degrees counterclockwise about the origin and then reflect the image in the x - axis. * (10 points)
a (3, -1), b (2, -3), c (1, 0)
a (3, 1), b (2, 3), c (1, 0)
a (-3, 1), b (-2, 3), c (-1, 0)
a (-3, -1), b (-2, -3), c (-1, 0)

Explanation:

Step1: Rotate the points 90 degrees counterclockwise

The rule for a 90 - degree counterclockwise rotation about the origin \((x,y)\to(-y,x)\)

• For point \(A(1,-3)\): \((1,-3)\to(3,1)\)
• For point \(B(3,-2)\): \((3,-2)\to(2,3)\)
• For point \(C(0,-1)\): \((0,-1)\to(1,0)\)

Step2: Reflect the rotated points over the \(x\) - axis

The rule for a reflection over the \(x\) - axis \((x,y)\to(x,-y)\)

• For the rotated point \(A'(3,1)\): \((3,1)\to(3, - 1)\)
• For the rotated point \(B'(2,3)\): \((2,3)\to(2,-3)\)
• For the rotated point \(C'(1,0)\): \((1,0)\to(1,0)\)

Answer:

A" \((3,-1)\), B" \((2,-3)\), C" \((1,0)\) (First option)