Question

question 2 points 2 a point p(2, 1) is rotated anticlockwise through 90 degrees and then reflected across the x - axis. what are the new coordinates of p (p)? o (1,2) o (-1,2) o (-1,-2) o (1,-2)

Explanation:

Step1: Rotate the point 90° counterclockwise

The rule for rotating a point \((x, y)\) 90° counterclockwise about the origin is \((x, y) \to (-y, x)\). Given the point \(P(2, 1)\), applying the rotation:
\(x = 2\), \(y = 1\), so the new coordinates after rotation are \((-1, 2)\).

Step2: Reflect the rotated point across the x - axis

The rule for reflecting a point \((x, y)\) across the x - axis is \((x, y) \to (x, -y)\). We have the rotated point \((-1, 2)\), applying the reflection:
\(x=-1\), \(y = 2\), so the new coordinates after reflection are \((-1, - 2)\).

Answer:

\((-1, -2)\) (corresponding to the option with coordinates \((-1, -2)\))