Question

identify the degree of rotation in both directions for the pictured rectangle, centered about the point $(1,0)$. recall that clockwise rotations are denoted with a negative degree.
(1 point)
the quadrilateral is rotated $square^{circ}$ counterclockwise or $square^{circ}$ clockwise.

Explanation:

Step1: Understand rotation properties of rectangle

A rectangle has rotational symmetry of order 2. The full - rotation is \(360^{\circ}\). For rotational symmetry of order \(n\), the angle of rotation \(\theta=\frac{360^{\circ}}{n}\). Here \(n = 2\), so \(\theta=\frac{360^{\circ}}{2}=180^{\circ}\)

Step2: Determine clockwise and counter - clockwise rotations

Since clockwise rotations are negative. A counter - clockwise rotation of \(180^{\circ}\) and a clockwise rotation of \(- 180^{\circ}\) (equivalent to \(180^{\circ}\) rotation in the opposite direction) will map the rectangle onto itself.

Answer:

The quadrilateral is rotated \(180^{\circ}\) counterclockwise or \(-180^{\circ}\) (or \(180^{\circ}\) clockwise in terms of magnitude) clockwise. So the blanks are filled with \(180\) and \(- 180\) (or \(180\) considering the magnitude for the clockwise part as the problem may just want the magnitude for the second blank if we consider the direction - sign convention. But strictly following the problem's instruction about clockwise being negative, \(-180\) is more accurate for the second blank)