Question

2 describe a sequence of transformations that takes trapezoid abcd to its image abcd * reflect over y-axis, translate right 6 units

Explanation:

Step1: Analyze Reflection over y - axis

A reflection over the \(y\) - axis changes the \(x\) - coordinate of a point \((x,y)\) to \((-x,y)\). For trapezoid \(ABCD\), let's consider the coordinates of its vertices. After reflecting over the \(y\) - axis, the left - hand side of the \(y\) - axis (where \(ABCD\) is initially) will be mirrored to the right - hand side (or vice - versa depending on the original position).

Step2: Analyze Translation Right 6 Units

A translation right by 6 units changes the \(x\) - coordinate of a point \((x,y)\) to \((x + 6,y)\). After reflecting over the \(y\) - axis, translating the resulting figure 6 units to the right will move the trapezoid to the position of \(A'B'C'D'\).

First, reflect trapezoid \(ABCD\) over the \(y\) - axis. This reflection maps each vertex \((x,y)\) of \(ABCD\) to \((-x,y)\). Then, translate the reflected trapezoid 6 units to the right. A translation 6 units to the right maps a point \((x,y)\) to \((x + 6,y)\). Combining these two transformations (reflection over \(y\) - axis followed by translation 6 units right) will take trapezoid \(ABCD\) to its image \(A'B'C'D'\).

Answer:

First, reflect Trapezoid \(ABCD\) over the \(y\) - axis. Then, translate the reflected trapezoid 6 units to the right.