Question

A quadrilateral with points A(1, 4), B(5, 4), C(4, 3) and D(2, 2) is reflected about the y-axis to form quadrilateral A'B'C'D'. Which of these sequences of transformations will also carry the quadrilateral ABCD onto A'B'C'D'? A. Rotating the quadrilateral 90˚ clockwise about the origin and then reflecting it across the x-axis B. Rotating the quadrilateral 180˚ about the origin and then reflecting it across the x-axis C. Rotating the quadrilateral 90˚ counterclockwise about the origin and then reflecting it across the line D. Rotating the quadrilateral 180˚ about the origin and then reflecting it across the line

Answer 1

(B)

Explanation:

I didn't see a graph plot out which line in (C) and (D) be across, but I think the answer is (B)

Original : A(1, 4), B(5, 4), C(4, 3) , D(2, 2)

After reflected about Y-axis: A'(-1, 4), B'(-5, 4), C'(-4, 3) , D'(-2, 2) ..........(1)

(B) Rotating the quadrilateral 180˚ about the origin

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

Reflecting it across the x-axis

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

The final coordinates are the same