Question

figure b is the result of a transformation on figure a. which transformation would accomplish this?
answer
a rotation 90°
counterclockwise
about the origin
a reflection over the
x - axis
a rotation 90°
clockwise about the
origin
a reflection over the
y - axis

Explanation:

Step1: Analyze reflection over y - axis

When a figure is reflected over the \(y\) - axis, the rule for a point \((x,y)\) in Figure \(A\) is transformed to \((-x,y)\).

Step2: Check the transformation

Looking at the positions of the vertices of Figure \(A\) and Figure \(B\), if we take a vertex of Figure \(A\) say \((x,y)\), its corresponding vertex in Figure \(B\) is \((-x,y)\). This is consistent with the reflection over the \(y\) - axis transformation.
For a \(90^{\circ}\) rotation (clockwise or counter - clockwise), the transformation rules are \((x,y)\to(y, - x)\) (clockwise) and \((x,y)\to(-y,x)\) (counter - clockwise), which do not match the given transformation from Figure \(A\) to Figure \(B\). For reflection over the \(x\) - axis, the rule is \((x,y)\to(x, - y)\) which also does not match.

Answer:

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