Question

clockwise about point ( p ) to create triangle ( def ). determine the correct orientation and location of triangle ( def )

Explanation:

Step1: Understand rotation concept

Rotation is a transformation that turns a figure around a fixed point (center of rotation). A \(90^{\circ}\) clock - wise rotation has a specific rule for coordinate transformation (if we consider coordinate - like positions relative to point \(P\)). For a point \((x,y)\) rotated \(90^{\circ}\) clock - wise about the origin \((0,0)\), the new coordinates are \((y, - x)\). In the context of the triangle, each vertex of \(\triangle ABC\) is rotated \(90^{\circ}\) clock - wise about point \(P\).

Step2: Analyze orientation

When a figure is rotated \(90^{\circ}\) clock - wise, its orientation changes. The side that was going in one direction (e.g., if we consider the order of vertices \(A - B - C\) in \(\triangle ABC\)) will have a new order of vertices \(D - E - F\) in \(\triangle DEF\) based on the rotation. The shape remains congruent (since rotation is a rigid transformation), but the position of each vertex relative to the center of rotation \(P\) changes. For example, if we assume some relative positions (like vertex \(A\) is to the right of \(P\) at a certain distance, after \(90^{\circ}\) clock - wise rotation, its image \(D\) will be below \(P\) at the same distance from \(P\) (in a simplified 2 - D plane assumption).

Step3: Match the rotated figure

By visual inspection (assuming standard rotation properties where each point of the triangle \(\triangle ABC\) is moved \(90^{\circ}\) clock - wise around \(P\)), we can see that the triangle with vertices \(E - D - F\) (in the order that matches the \(90^{\circ}\) clock - wise rotation from \(\triangle ABC\)) is the correct one. The first two triangles (with \(F\) on the left and right in a non - rotated - correctly - oriented way) are incorrect. The third triangle (with vertices \(E - D - F\) in the proper \(90^{\circ}\) clock - wise rotated orientation relative to the original \(\triangle ABC\) around \(P\)) is the right choice.

Answer:

The triangle with vertices \(E - D - F\) (the third triangle among the three small triangles) is the correct orientation and location of \(\triangle DEF\) after a \(90^{\circ}\) clock - wise rotation about point \(P\) of \(\triangle ABC\).