Question

rotation 5
the shape is rotated clockwise 90 degrees around the origin.
can you find the new points?
can you write the rule?
what did you notice?
the new points are...
the rule is (x,y) →...
i noticed...

Explanation:

Step1: Recall 90° clockwise rotation rule

For a point \((x, y)\), rotating 90° clockwise around the origin transforms it to \((y, -x)\).

Step2: Apply rule to each point

• For \((2, 6)\): Substitute \(x = 2\), \(y = 6\) into \((y, -x)\), get \((6, -2)\).
• For \((4, 4)\): Substitute \(x = 4\), \(y = 4\) into \((y, -x)\), get \((4, -4)\).
• For \((6, 8)\): Substitute \(x = 6\), \(y = 8\) into \((y, -x)\), get \((8, -6)\).

Step3: State the rule

The rule for 90° clockwise rotation about the origin is \((x, y) \to (y, -x)\).

Step4: Note observations

Notice that the \(x\) and \(y\) coordinates swap, and the new \(x\) (original \(y\)) stays positive, new \(y\) (negative original \(x\)) is negative for these points (since original \(x\) was positive).

Answer:

The new points are \((6, -2)\), \((4, -4)\), \((8, -6)\).
The rule is \((x, y) \to (y, -x)\).
I noticed that the \(x\) and \(y\) coordinates of each point are swapped, and the sign of the original \(x\)-coordinate is flipped (becomes negative) for the new \(y\)-coordinate.