Question

answer
a reflection over the y - axis a reflection over the x - axis
a rotation, 90° clockwise about the origin a translation 4 units down

Explanation:

Step1: Analyze reflection over x - axis

A reflection over the \(x\) - axis changes the sign of the \(y\) - coordinate of a point \((x,y)\) to \((x, - y)\). Looking at the two figures, we can check the coordinates of corresponding vertices. If we take a vertex of the upper figure and reflect it over the \(x\) - axis, we get the corresponding vertex of the lower figure. For example, if a point on the upper figure is \((x,y)\), after reflection over \(x\) - axis, it becomes \((x, - y)\), which matches the position of the corresponding point on the lower figure.

Step2: Eliminate other options

• Reflection over \(y\) - axis: A reflection over \(y\) - axis changes \((x,y)\) to \((-x,y)\), which does not match the transformation between the two figures.
• Rotation \(90^{\circ}\) about origin: A \(90^{\circ}\) rotation about the origin changes \((x,y)\) to \((-y,x)\) (counter - clockwise) or \((y, - x)\) (clockwise), which is not the case here.
• Translation 4 units down: A translation 4 units down changes \((x,y)\) to \((x,y - 4)\), but the symmetry about the \(x\) - axis is more evident from the vertical flip of the figures.

Answer:

A reflection over the \(x\) - axis