Question

question 14 (multiple choice worth 1 points) (02.01r, 02.02r mc) which sequence of transformations will map figure k onto figure k? reflection across x = 4, 180° rotation about the origin, and a translation of (x + 8, y) reflection across x = 4, 180° rotation about the origin, and a translation of (x - 8, y) reflection across y = 4, 180° rotation about the origin, and a translation of (x + 8, y) reflection across y = 4, 180° rotation about the origin and a translation of (x - 8, y)

Explanation:

Step1: Analyze reflection

The figure K and K' seem to be symmetric about a vertical - like line. A reflection across \(x = 4\) can start the transformation. When reflecting a point \((x,y)\) across the line \(x = a\), the new \(x\) - coordinate is \(2a - x\).

Step2: Analyze rotation

A \(180^{\circ}\) rotation about the origin changes the sign of both \(x\) and \(y\) coordinates of a point \((x,y)\) to \((-x,-y)\).

Step3: Analyze translation

After reflection and rotation, to map the figure to the correct position, we need to translate. Observing the horizontal shift, we note that a translation of \((x - 8,y)\) is required.

Answer:

Reflection across \(x = 4\), \(180^{\circ}\) rotation about the origin, and a translation of \((x - 8,y)\)