Question

Which statement accurately explains whether a reflection over the y-axis and a 270° counterclockwise rotation would map figure ACB onto itself? a coordinate plane with figure ACB with point A at 1, 1, C at 3, 4 and B at 5, 1 Yes, A″C″B″ is located at A″(1, 1), C″(4, 3), and B″(1, 5) Yes, A″C″B′ is located at A″(1, 1), C″(3, 4), and B″(5, 1) No, A″C″B″ is located at A″(1, 1), C″(4, 3), and B″(1, 5) No, A″C″B″ is located at A″(1, 1), C″(3, 4), and B″(5, 1)

Answer 1

Answer:

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

Step-by-step explanation:

The triangle has vertices A(1,1), B(5,1), C(3,4).

First transformation is reflection over y-axis with 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)

Second transformation is rotation by 270° counterclockwise with the rule

(x,y)→(y,-x)

so

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

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