Question

select the correct answer.

which image shows the triangle rotated \\(90^\circ\\) clockwise about point \\(p\\)?

Explanation:

Identify the original orientation

Using the Geometric Transformations knowledge point

• The original figure is a right triangle with a vertical leg on the left and a horizontal leg at the bottom.
• Point \(P\) is located directly below the vertical leg of the triangle.

Analyze the rotation direction

Using the Rotations in the Coordinate Plane knowledge point

• A \(90^\circ\) clockwise rotation turns the figure a quarter-turn to the right.
• The vertical leg (pointing up) rotates to become horizontal (pointing right).
• The horizontal leg (pointing right) rotates to become vertical (pointing down).

Determine the position relative to point P

Using the Rotations in the Coordinate Plane knowledge point

• Since point \(P\) is directly below the vertical leg, rotating the entire system \(90^\circ\) clockwise about \(P\) means:
• The line segment connecting the triangle to \(P\) rotates \(90^\circ\) clockwise.
• Therefore, the triangle moves from being above \(P\) to being to the right of \(P\).
• Point \(P\) will now be located to the left of the rotated triangle.

Match with the options

Using the Geometric Transformations knowledge point

• Option 1: The triangle is to the left of \(P\), which is incorrect.
• Option 2: The triangle is to the right of \(P\), and its orientation shows the long leg is horizontal and the short leg is vertical on the right. This matches a \(90^\circ\) clockwise rotation.
• Option 3: The triangle is below \(P\), which is incorrect.
• Option 4: The triangle is above \(P\), which is incorrect.

Answer:

• (A) Triangle to the left of point P
• (B) Triangle to the right of point P, with the long leg horizontal and point P to its left (Correct answer)
• (C) Triangle below point P
• (D) Triangle above point P