Question

1. which figure shows the triangle below reflected over the x - axis, then reflected over the y - axis?

Explanation:

Step1: Reflect over the x - axis

When reflecting a point \((x,y)\) over the \(x\) - axis, the transformation rule is \((x,y)\to(x, - y)\). This flips the figure vertically.

Step2: Reflect over the y - axis

After the first reflection, when reflecting the resulting point \((x,-y)\) over the \(y\) - axis, the transformation rule is \((x,-y)\to(-x,-y)\). This flips the figure horizontally.

Combining these two reflections (over \(x\) then \(y\)) is equivalent to a rotation of \(180^{\circ}\) about the origin. Looking at the options, option D shows the triangle in the position that would result from first reflecting over the \(x\) - axis (flipping it down) and then over the \(y\) - axis (flipping it to the left).

Answer:

D.