Question

which two series of transformations would carry triangle abc to triangle pqr? a. a translation 2 units right followed by a translation 2 units down b. a translation 6 units right followed by a translation 2 units down c. a 180° rotation about point b followed by a translation 2 units right and 2 units down d. a reflection across a horizontal line 1 unit below (overline{bc}) followed by a rotation 180° about point b e. a reflection across a horizontal line 1 unit below (overline{bc}) followed by a reflection across a vertical line 1 unit right of point b

Explanation:

Step1: Analyze option A

A translation 2 units right and 2 units down won't map triangle ABC to triangle PQR as the position is incorrect.

Step2: Analyze option B

Count the horizontal and vertical displacements. A translation 6 units right and 2 units down aligns the triangles correctly.

Step3: Analyze option C

A 180 - degree rotation about point B changes the orientation in a way that 2 units right and 2 units down won't map to PQR.

Step4: Analyze option D

A reflection across a horizontal line 1 unit below BC followed by a 180 - degree rotation about point B won't give the correct orientation and position.

Step5: Analyze option E

A reflection across a horizontal line 1 unit below BC followed by a reflection across a vertical line 1 unit right of point B won't map the triangles correctly.

Answer:

B. a translation 6 units right followed by a translation 2 units down