Question

question 9 (multiple choice worth 4 points) 02 021 mc carlos performed a transformation on trapezoid efgh to create efgh, as shown in the figure below: what transformation did carlos perform to create efgh? rotation of 270° clockwise about the origin reflection across the x - axis rotation of 90° clockwise about the origin reflection across the line of symmetry of the figure

Explanation:

Step1: Recall reflection rule

When a point \((x,y)\) is reflected across the \(x -\)axis, the transformation rule is \((x,y)\to(x, - y)\).

Step2: Analyze the figure

Looking at the trapezoid \(EFGH\) and \(E'F'G'H'\), if we assume a general point \((x,y)\) on \(EFGH\) and its corresponding point \((x,-y)\) on \(E'F'G'H'\). For example, if we consider the vertical distance from a point on \(EFGH\) to the \(x -\)axis and the vertical distance from its corresponding point on \(E'F'G'H'\) to the \(x -\)axis, they are equal in magnitude but opposite in sign.

Step3: Eliminate other options

• For a rotation of \(270^{\circ}\) clockwise about the origin, the transformation rule is \((x,y)\to(y,-x)\).
• For a rotation of \(90^{\circ}\) clockwise about the origin, the transformation rule is \((x,y)\to(-y,x)\).
• A reflection across the line of symmetry of the figure (if it was a non - \(x\) axis line of symmetry) would not follow the \((x,y)\to(x, - y)\) pattern as clearly as the \(x -\)axis reflection.

Answer:

Reflection across the \(x -\)axis.