Question

Identify the mapping as a translation, reflection, rotation, or glide reflection. Find the translation rule, reflection line, center of rotation, and angle of rotation, or glide translation rule and reflection line.

ΔHGF→ΔHIF

A. Translation, Translation rule: IF, Reflection line: None, Center of rotation: None, Angle of rotation: None
B. Reflection, Translation rule: None, Reflection line: IF, Center of rotation: None, Angle of rotation: None
C. Rotation, Translation rule: None, Reflection line: None, Center of rotation: H, Angle of rotation: 180 degrees
D. Glide Reflection, Translation rule: IH, Reflection line: IH, Center of rotation: None, Angle of rotation: None

Answer 1

To determine the transformation from ΔHGF to ΔHIF, it appears to be a rotation by 180 degrees about point H, which maps ΔHGF onto ΔHIF without any translation or reflection.

Step-by-step explanation:

To identify the mapping of ΔHGF to ΔHIF as a translation, reflection, rotation, or glide reflection, we must look at the characteristics of the transformation.

For a translation, there would be a vector rule that moves every point of the figure the same distance in the same direction. A reflection would involve a line over which the figure is flipped, producing a mirror image. A rotation means the figure is turned around a fixed point through a given angle. Lastly, a glide reflection is a transformation involving a translation followed by a reflection over a line parallel to the direction of the translation.

Considering the options given, we need to choose the one that accurately describes the transformation from ΔHGF to ΔHIF. After examining the given options, Option C seems the most plausible as it A rotation around point H by an angle of 180 degrees with no translation or reflection would map ΔHGF onto ΔHIF.