Question

tify the transformation that maps the figure onto itself
a rotate 360° clockwise about (-4,-3) and reflect across the line y = -6
b rotate 360° clockwise about (-4,-3) and reflect across the line x = -4
c rotate 180° clockwise about (-1,-6) and reflect across the line y = -6
d rotate 180° clockwise about (-1,-6) and reflect across the line x = -4

Explanation:

Step1: Analyze rotation

A \(360^{\circ}\) rotation about any point maps a figure onto itself. A \(180^{\circ}\) rotation about a non - center of symmetry may not map the trapezoid onto itself.

Step2: Analyze reflection

For a reflection to map the trapezoid onto itself, the line of reflection should be a line of symmetry. The vertical line \(x = - 4\) is a line of symmetry for the trapezoid (assuming the trapezoid is symmetric about \(x=-4\) as per its position in the coordinate - plane). The line \(y=-6\) is not a line of symmetry for the trapezoid shown.

Answer:

B. rotate \(360^{\circ}\) clockwise about \((-4,-3)\) and reflect across the line \(x = - 4\)