Question

Analyze the pre-image ABCD. What are the vertices of the final image if T -1. -2 ° r y=x? Option 1: A'(-1, 3), B'(-2, 2), C'(-3, 1), D'(-4, 0) Option 2: A'(-2, 1), B'(-3, 0), C'(-4, -1), D'(-5, -2) Option 3: A'(-1, -2), B'(-2, -3), C'(-3, -4), D'(-4, -5) Option 4: A'(1, -2), B'(2, -3), C'(3, -4), D'(4, -5)

Answer 1

The vertices of the final image are A'(-1, -2), B'(-2, -3), C'(-3, -4), D'(-4, -5).

Step-by-step explanation:

The pre-image ABCD is transformed by the transformation T: (x, y) → (-y, x). Since T -1 represents the inverse of T, the vertices of the final image are obtained by applying the inverse transformation to the pre-image.

Using the inverse transformation, the vertices of the final image are:

• A'(-1, -2)
• B'(-2, -3)
• C'(-3, -4)
• D'(-4, -5)

Therefore, Option 3: A'(-1, -2), B'(-2, -3), C'(-3, -4), D'(-4, -5) is the correct answer.