Question

drag the image to the correct location. not all tiles will be used. triangle abc is rotated 90° clockwise about point p to create triangle def. determine the correct orientation and location of triangle def.

Explanation:

Step1: Recall 90° clockwise rotation

A 90° clockwise rotation about a point \( P \) transforms a point \((x,y)\) relative to \( P \) to \((y, -x)\) (in coordinate terms, but visually, we can track the orientation). For triangle \( ABC \), rotating 90° clockwise about \( P \) will change the direction of the vertices.

Step2: Analyze the triangles

• The first triangle (top right with \( F \) above \( DE \)): Orientation doesn't match 90° clockwise.
• The second triangle (middle right with \( F \) below \( DE \)): Let's check the original triangle \( ABC \) (with \( A \), \( B \), \( C \)). Rotating 90° clockwise, the "top" vertex (relative to \( P \)) should move to a position that makes the base \( DE \) horizontal (or as per rotation) and the third vertex below. Wait, actually, when rotating 90° clockwise, the triangle's orientation should have the side corresponding to \( AB \) (or \( AC \)) rotated such that the angle changes. Wait, maybe better to look at the third triangle (bottom right) with \( E \), \( F \), \( D \). Wait, no—wait, the second triangle (middle right: \( D \), \( E \) horizontal, \( F \) below) is the result of rotating \( ABC \) 90° clockwise about \( P \). Let's visualize: original \( ABC \) has \( A \), \( B \), \( C \) with \( A \) at the bottom, \( B \) top left, \( C \) top right. Rotating 90° clockwise about \( P \), the new triangle \( DEF \) should have \( D \), \( E \) horizontal (like \( AB \) was, but rotated) and \( F \) below, matching the middle right triangle. Wait, no—wait, the bottom right triangle has \( E \) and \( D \) with \( F \) on the left, which is a 90° counterclockwise? No, 90° clockwise: if you take a triangle and rotate 90° clockwise, the vertices' order (clockwise/counterclockwise) and their positions relative to the base. Wait, the correct triangle is the middle one (second from top on the right: \( D \) and \( E \) horizontal, \( F \) below). Because rotating 90° clockwise, the "apex" (like \( C \) or \( B \)) moves to below the base \( DE \) (which was \( AB \) or \( AC \) in original). So the correct triangle is the middle one (the second triangle on the right, with \( D \) and \( E \) horizontal, \( F \) below \( DE \)).

Answer:

The Middle Graph (the second triangle on the right, with vertices \( D \), \( E \) (horizontal), and \( F \) below \( DE \))