Question

find the coordinates of the figure with the given coordinates after the transformation on the plane.
preimage: ( a(1,3), b(1,1), c(4,1) )
image: triangle ( def ), rotation of ( abc 270^{circ} ) counterclockwise about the origin

Explanation:

Step1: Recall rotation formula

The formula for a \(270^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(y, - x)\)

Step2: Apply formula to point \(A(1,3)\)

For \(A(1,3)\), using the formula \((x = 1,y = 3)\), we get \(D(3,-1)\)

Step3: Apply formula to point \(B(1,1)\)

For \(B(1,1)\), using the formula \((x = 1,y = 1)\), we get \(E(1,-1)\)

Step4: Apply formula to point \(C(4,1)\)

For \(C(4,1)\), using the formula \((x = 4,y = 1)\), we get \(F(1,-4)\)

Answer:

\(D(3,-1)\), \(E(1,-1)\), \(F(1,-4)\)