Question

a double reflection over the x - and y - axes is the same as a __________ of ______
reflection over the x - axis
rotation of 180 degrees
rotation of 90 degrees
reflection over the y - axis

Explanation:

Let's consider a point \((x,y)\) in the coordinate plane.

• First reflection (over the \(x -\)axis):

When we reflect a point \((x,y)\) over the \(x -\)axis, the transformation rule is \((x,y)\to(x, - y)\).

• Second reflection (over the \(y -\)axis):

When we reflect the point \((x,-y)\) (the result of the first reflection) over the \(y -\)axis, the transformation rule is \((x,-y)\to(-x,-y)\).

• Rotation of \(180^{\circ}\):

The transformation rule for a rotation of \(180^{\circ}\) about the origin is \((x,y)\to(-x,-y)\).

A reflection over the \(x -\)axis followed by a reflection over the \(y -\)axis has the same effect as a rotation of \(180^{\circ}\) about the origin.

Answer:

B. Rotation of 180 Degrees