Question

which of the following transformation will map the trapezoid onto itself? rotation 90 degrees about (2,-1) reflection across green line x axis reflection reflection across the blue line

Explanation:

Step1: Analyze rotation

A \(90^{\circ}\) rotation about \((2, - 1)\) will change the orientation of the trapezoid. So it won't map the trapezoid onto itself.

Step2: Analyze \(x -\)axis reflection

An \(x -\)axis reflection will flip the trapezoid vertically. Since the trapezoid is not symmetric about the \(x -\)axis, it won't map onto itself.

Step3: Analyze reflection across an arbitrary green line

If the green line is not a line of symmetry (and without seeing the exact position, but based on general properties of trapezoids which are not symmetric in a non - special case for a random green line), a reflection across a non - symmetry green line won't map the trapezoid onto itself.

Step4: Analyze reflection across the blue line

If the blue line is the vertical line passing through the mid - points of the non - parallel sides (the line of symmetry of the trapezoid), a reflection across this line (a line of symmetry) will map the trapezoid onto itself.

Answer:

reflection across the blue line