Question

Which figure can be transformed into figure P by a translation 2 units to the right followed by a reflection across the x-axis?

Answer 1

Figure M

Explanation:

Figure P has vertices at points (-2,4), (-2,8), (-6,8) and (-6,6).

Consider figure M with vertices (-4,-4), (-4,-8), (-8,-8) and (-8,-6).

1. Translate figure M 2 units to the right. This translation has the rule:

(x,y)→(x+2,y),

so

• (-4,-4)→(-2,-4);
• (-4,-8)→(-2,-8);
• (-8,-8)→(-6,-8);
• (-8,-6)→(-6,-6).

2. Reflect the translation image figure M across the x-axis according to the rule

(x,y)→(x,-y)

Thus,

• (-2,-4)→(-2,4);
• (-2,-8)→(-2,8);
• (-6,-8)→(-6,8);
• (-6,-6)→(-6,6).