Question

animate rotation again
pre-image image
(-4,1) → (□,□)
(-1,2) → (□,□)
(-4,4) → (□,□)
(-7,4) → (□,□)

Explanation:

Step1: Identify Rotation Center

The rotation is about the origin \((0,0)\) (yellow dot).

Step2: Determine Rotation Direction/Angle

From pre - image (red) to image (blue), observe the rotation. Let's assume it's a \(90^{\circ}\) clockwise rotation. The rule for \(90^{\circ}\) clockwise rotation about the origin is \((x,y)\to(y, - x)\).

Step3: Apply Rotation to \((-4,1)\)

Using the rule \((x,y)\to(y, - x)\), for \((-4,1)\), \(x=-4,y = 1\). So the image is \((1,4)\).

Step4: Apply Rotation to \((-1,2)\)

For \((-1,2)\), \(x=-1,y = 2\). Using the rule, the image is \((2,1)\).

Step5: Apply Rotation to \((-4,4)\)

For \((-4,4)\), \(x = - 4,y=4\). The image is \((4,4)\).

Step6: Apply Rotation to \((-7,4)\)

For \((-7,4)\), \(x=-7,y = 4\). The image is \((4,7)\).

Answer:

\((-4,1)\to(1,4)\)
\((-1,2)\to(2,1)\)
\((-4,4)\to(4,4)\)
\((-7,4)\to(4,7)\)