Question

answer
a reflection over the x - axis
a translation 1 unit right and 4
units up
a translation 4 units left and 1
unit down
a reflection over the y - axis
submit answer

Explanation:

Step1: Recall reflection over x - axis

If a point \((x,y)\) is reflected over the \(x\) - axis, the new point is \((x, - y)\).

Step2: Recall reflection over y - axis

If a point \((x,y)\) is reflected over the \(y\) - axis, the new point is \((-x,y)\).

Step3: Recall translation rules

A translation \(a\) units right and \(b\) units up transforms a point \((x,y)\) to \((x + a,y + b)\); a translation \(a\) units left and \(b\) units down transforms a point \((x,y)\) to \((x - a,y - b)\).

Step4: Analyze the given figures

Let's take a vertex of the upper - left figure (say \((-4,4)\)) and the corresponding vertex of the lower - left figure (say \((-4,-4)\)). If we consider reflection over the \(x\) - axis: for a point \((x,y)\) reflected over the \(x\) - axis, we get \((x,-y)\). Here, when \(x=-4\) and \(y = 4\), the reflection is \((-4,-4)\).

Answer:

A reflection over the \(x\) - axis