Question

triangle p undergoes a sequence of transformations resulting in triangle q. which sequence of transformations could be used to show that triangle q is similar but not congruent to triangle p?
a a reflection followed by a translation
b a rotation followed by a reflection
c a reflection followed by a rotation
d a translation followed by a dilation

Explanation:

Step1: Understand congruence and transformations

Congruent triangles have the same shape and size. Transformations like translation (sliding), rotation (turning), and reflection (flipping) preserve congruence. Dilation (scaling) changes the size.

Step2: Analyze each option

• Option A: Reflection followed by translation. Both reflection and translation are rigid motions (preserve congruence).
• Option B: Rotation followed by reflection. Both rotation and reflection are rigid motions (preserve congruence).
• Option C: Reflection followed by rotation. Both reflection and rotation are rigid motions (preserve congruence).
• Option D: Translation followed by dilation. Dilation changes the size of the triangle. If there is a dilation, the two triangles (original \(P\) and final \(Q\)) will not be congruent.

Answer:

D. a translation followed by a dilation