Question

etermining the type of transformation
a transformation is shown in the diagram.
∠a≅∠a and ∠c≅∠c
which transformation is shown in the figure?
△abc was translated to form △abc. the transformation is not isometric.
△abc was reflected to form △abc. the transformation is isometric.
△abc was rotated to form △abc. the transformation is isometric.
△abc was dilated to form △abc. the transformation is not isometric.

Explanation:

Step1: Recall transformation types

Translation moves a figure without rotation or reflection. Reflection flips a figure over a line. Rotation turns a figure around a point. Dilation changes the size of a figure. Isometric transformations preserve shape and size (translation, reflection, rotation).

Step2: Analyze the triangles

The orientation of $\triangle ABC$ has changed to form $\triangle A'B'C'$, which rules out translation. The size has not changed, ruling out dilation. The change in orientation indicates a rotation. Rotation is an isometric transformation.

Answer:

$\triangle ABC$ was rotated to form $\triangle A'B'C'$. The transformation is isometric.