Question

show what you know! after a rectangle with vertices (1,2), (1,4), (3,4), (3,2) is rotated 90° clockwise and then translated 3 units to the right, what are the new coordinates? (3,1), (5,1), (5,3), (3,3) (5, -1), (7, -1), (7, -3), (5, -3) (4,2), (2,4), (2,2), (4,0) (1,2), (1,4), (3,4), (3,2)

Explanation:

Step1: Apply rotation formula

The formula for a \(90^{\circ}\) clockwise rotation \((x,y)\to(y, -x)\).
For \((1,2)\): \(x = 1,y = 2\), after rotation \((2,-1)\)
For \((1,4)\): \(x = 1,y = 4\), after rotation \((4,-1)\)
For \((3,4)\): \(x = 3,y = 4\), after rotation \((4,-3)\)
For \((3,2)\): \(x = 3,y = 2\), after rotation \((2,-3)\)

Step2: Apply translation

The translation rule is \((x,y)\to(x + 3,y)\)
For \((2,-1)\): \(x=2 + 3=5,y=-1\) \(\to(5,-1)\)
For \((4,-1)\): \(x=4 + 3=7,y=-1\) \(\to(7,-1)\)
For \((4,-3)\): \(x=4 + 3=7,y=-3\) \(\to(7,-3)\)
For \((2,-3)\): \(x=2 + 3=5,y=-3\) \(\to(5,-3)\)

Answer:

\([(5,-1),(7,-1),(7,-3),(5,-3)]\)