Question

drag the image to the correct location. not all tiles will be used.

triangle abc is rotated \\(90^\circ\\) clockwise about point p to create triangle def. determine the correct orientation and location of triangle def.

Explanation:

Identify the rotation parameters

Using the Rotations in the Coordinate Plane and Geometric Transformations knowledge points

• Pre-image: Triangle \(ABC\)
• Center of rotation: Point \(P\)
• Angle and direction: \(90^\circ\) clockwise

Determine the target location

Using the Rotations in the Coordinate Plane knowledge point

• Point \(P\) is to the right of triangle \(ABC\).
• A \(90^\circ\) clockwise rotation about \(P\) moves the figure from the left of \(P\) to the region directly above \(P\).
• Therefore, the correct target location is the top dashed box.

Determine the correct orientation

Using the Geometric Transformations knowledge point

• In triangle \(ABC\), the horizontal base is \(BA\) (with \(B\) on the left, \(A\) on the right), and vertex \(C\) points upwards.
• Rotating \(90^\circ\) clockwise turns the horizontal base \(BA\) into a vertical segment.
• The vertex \(C\) (pointing up) rotates \(90^\circ\) clockwise to point to the right.
• The base \(BA\) rotates to become vertical on the left, with \(B\) moving to the top and \(A\) moving to the bottom.
• Mapping vertices \(A \to D\), \(B \to E\), \(C \to F\):
• \(B\) (top) becomes \(E\).
• \(A\) (bottom) becomes \(D\).
• \(C\) (right) becomes \(F\).
• This matches the second tile from the left: a triangle pointing to the right with vertical side \(ED\) on the left (\(E\) at the top, \(D\) at the bottom) and vertex \(F\) on the right.

Answer:

• Correct Location: The top dashed box (directly above point \(P\)).
• Correct Tile (Orientation): The second tile from the left, which shows triangle \(DEF\) pointing to the right, with vertical side \(ED\) on the left (\(E\) at the top, \(D\) at the bottom) and vertex \(F\) on the right.