Question

Which statement accurately explains whether a reflection over the x-axis and a 180° rotation would map figure ACB onto itself?

Answer 1

Answer: A)  No, A″C″B″ is located at A″(−1, 1), C″(−3, 4), and B″(−5, 1)

Answer 2

Answer:

A

Step-by-step explanation:

Triangle ABC has vertices A(1,1), B(5,1) and C(3,4).

Reflectio across the x-axis has the rule:

(x,y)→(x,-y),

so

• A(1,1)→A'(1,-1)
• B(5,1)→B'(5,-1)
• C(3,4)→C'(3,-4)

Rptation by 180° has the rule

(x,y)→(-x,-y),

so

• A'(1,-1)→A''(-1,1)
• B'(5,-1)→B''(-5,1)
• C'(3,-4)→C''(-3,4)

These points A'', B'', C'' differ from original vertices, so the image triangle is not the same as the pre-image triangle.