2015 AMC 10B Problem 8

Question

The letter F shown below is rotated

90^\circ

clockwise around the origin, then reflected in the

y

-axis, and then rotated a half turn around the origin. What is the final image?

Track what happens to the axes under the three transformations

A half turn after a

y

-reflection is a reflection in the

x

-axis

The first rotation puts the F below the

x

-axis.

A half turn is equivalent to reflecting in both coordinate axes. Therefore the final half turn cancels the preceding reflection in the

y

-axis and leaves a reflection in the

x

-axis.

Reflecting the rotated figure in the

x

-axis produces choice E.

Thus, the correct answer is E .

Problem 8 in other years