Question

persevere if pqrs is translated along (3, -2), reflected in y = -1, and rotated 90° about the origin, what are the coordinates of pqrs?

Explanation:

Step1: Find coordinates after translation

Translation rule \((x,y)\to(x + 3,y-2)\).
Original coordinates: \(P(-4,1)\), \(Q(-1,2)\), \(R(0,0)\), \(S(-2,-2)\)
After translation:
\(P'(-4 + 3,1-2)=(-1,-1)\)
\(Q'(-1 + 3,2-2)=(2,0)\)
\(R'(0 + 3,0-2)=(3,-2)\)
\(S'(-2 + 3,-2-2)=(1,-4)\)

Step2: Find coordinates after reflection

Reflection rule over \(y=-1\): \((x,y)\to(x,-2 - y)\)
After reflection:
\(P''(-1,-2-(-1))=(-1,-1)\)
\(Q''(2,-2 - 0)=(2,-2)\)
\(R''(3,-2-(-2))=(3,0)\)
\(S''(1,-2-(-4))=(1,2)\)

Step3: Find coordinates after rotation

Rotation rule \(90^{\circ}\) about origin: \((x,y)\to(-y,x)\)
After rotation:
\(P'''(1,-1)\)
\(Q'''(2,2)\)
\(R'''(0,3)\)
\(S'''(-2,1)\)

Answer:

\(P'''(1,-1)\), \(Q'''(2,2)\), \(R'''(0,3)\), \(S'''(-2,1)\)