Question

which is a transformation of the triangle abc into 6 units
so the right and rotated 90 degrees clockwise about the origin?

Explanation:

Step1: Understand rotation rules

When a figure is rotated 90 degrees clockwise about the origin \((x,y)\to(y, -x)\). Also, translation 6 units to the right means \((x,y)\to(x + 6,y)\).

Step2: Analyze each option

• For option A: The transformation does not follow the combined rule of 90 - degree clockwise rotation and 6 - unit right translation.
• For option B: First, assume a point \((x,y)\) on the original triangle. After 90 - degree clockwise rotation \((x,y)\to(y,-x)\), then after translation 6 units to the right \((y,-x)\to(y + 6,-x)\). This option follows the correct transformation rule.
• For option C: The orientation and position do not match the result of 90 - degree clockwise rotation and 6 - unit right translation.
• For option D: The orientation and position do not match the result of 90 - degree clockwise rotation and 6 - unit right translation.

Answer:

B.