Question

look at this diagram:
diagram of quadrilateral fghi
which diagram shows quadrilateral fghi rotated 60° counterclockwise about i?

Explanation:

Step1: Recall Rotation Rules

A counterclockwise rotation about a point \( I \) means each vertex (except \( I \), which stays fixed) is rotated \( 60^\circ \) counterclockwise around \( I \). The distance from \( I \) to each vertex ( \( F, G, H \)) should remain the same, and the angle between \( \overline{IF} \) and its image \( \overline{IF'} \) (and similarly for other vertices) should be \( 60^\circ \) counterclockwise.

Step2: Analyze the First Option

In the first diagram (with blue and red figures), vertex \( I \) is fixed. The segments \( IF, IG, IH \) and their images \( IF', IG', IH' \) should have the same length, and the angle of rotation ( \( 60^\circ \) counterclockwise) should be consistent. Checking the positions, the blue figure (image) has \( I \) fixed, and the rotation of \( F, G, H \) around \( I \) by \( 60^\circ \) counterclockwise seems to match: the distance from \( I \) to \( F' \), \( G' \), \( H' \) is equal to \( I \) to \( F \), \( G \), \( H \), and the angle between \( IF \) and \( IF' \) (visually) is \( 60^\circ \) counterclockwise.

Step3: Analyze the Second Option

In the second diagram, \( I \) is not fixed (it has moved to \( I' \)), which violates the rotation about \( I \) (the center of rotation should be fixed). So this option is incorrect.

Answer:

The first diagram (the one with the blue and red quadrilaterals, where \( I \) is fixed and the image is rotated \( 60^\circ \) counterclockwise around \( I \))