Question

question 1
choose one composition of transformations that would create a rigid transformation.

a rotation of 135° followed by dilation of scale factor 3

a reflection across x - axis followed by a rotation of 360°

a translation of 4 units to the left followed by dilation of scale factor 8

a dilation of scale factor by 2 followed by a translation of 3 units to the right

Explanation:

Step1: Recall Rigid Transformation

Rigid transformations (isometries) preserve distance and shape. They include translation, rotation, reflection. Dilation is non - rigid (changes size).

Step2: Analyze Each Option

• Option 1: Rotation (rigid) followed by dilation (non - rigid). So the composition is non - rigid.
• Option 2: Reflection (rigid) followed by rotation of \(360^{\circ}\) (which is equivalent to the identity transformation, also rigid). Both are rigid, so composition is rigid.
• Option 3: Translation (rigid) followed by dilation (non - rigid). Composition is non - rigid.
• Option 4: Dilation (non - rigid) followed by translation (rigid). Composition is non - rigid.

Answer:

B. A reflection across x - axis followed by a rotation of \(360^{\circ}\)