Question

figure c is the result of a transformation on figure b. which transformation would accomplish this?
answer
a rotation 180° counterclockwise
about the origin
a reflection over the x - axis
a translation 2 units to the left.
a reflection over the y - axis

Explanation:

Step1: Recall transformation rules

• Rotation \(180^{\circ}\) counter - clockwise about the origin: \((x,y)\to(-x,-y)\)
• Reflection over \(x -\)axis: \((x,y)\to(x, - y)\)
• Translation \(2\) units to the left: \((x,y)\to(x - 2,y)\)
• Reflection over \(y -\)axis: \((x,y)\to(-x,y)\)

Step2: Analyze the positions of points

Let's assume a general point \((x,y)\) in Figure \(B\). In Figure \(C\), if we consider the \(x -\)coordinate, for example, if a point in Figure \(B\) has \(x = 1\), in Figure \(C\) the corresponding \(x=-1\). The \(y -\)coordinate remains the same.

Answer:

A reflection over the \(y -\)axis.