Question

fluency

1. given the circle centered at c shown below and marked point a, use your protractor and a straightedge to locate each of the following image points.

(a) the image of point a after a clockwise rotation about point c by ( 90^{circ} ). label this point b.
(b) the image of point a after a clockwise rotation about point c by ( 130^{circ} ). label this point d.
(c) the image of point a after a counterclockwise rotation about point c by ( 60^{circ} ). label this point e.
(d) the image of point a after a rotation about point c by ( 180^{circ} ). label this point f.

1. if point e is rotated about point q by ( 50^{circ} ) and its image point is ( e ), then which of the following would be true about the lengths of ( overline{qe} ) and ( overline{qe} )?

(1) they are the same length
(2) ( overline{qe} ) is shorter than ( overline{qe} )
(3) ( overline{qe} ) is longer than ( overline{qe} )
(4) a comparison cannot be made based on the information given

1. if point g is mapped to point h by a ( 180^{circ} ) rotation about point m, then which of the following statement is true?

(1) ( overline{gm} perp overline{hm} )
(2) ( overline{gm} parallel overline{hm} )
(3) g, h, and m are collinear
(4) ( gh = gm )

1. point ( g ) is the image of point g after a clockwise rotation of ( 68^{circ} ) about point c. which of the following counterclockwise rotations about c would map g onto ( g )?

(1) a rotation of ( 22^{circ} )
(2) a rotation of ( 34^{circ} )
(3) a rotation of ( 112^{circ} )
(4) a rotation of ( 292^{circ} )

Explanation:

• Question 2: Rotation is a rigid transformation. In a rigid transformation, the distance from the center of rotation to a point and its image is preserved. So, for a rotation about point \(Q\) of point \(E\) to \(E'\), \(|\overline{QE}| = |\overline{QE'}|\).
• Question 3: When a point \(G\) is mapped to point \(H\) by a \(180^{\circ}\) rotation about point \(M\), the points \(G\), \(M\), and \(H\) lie on a straight - line. That is, \(G\), \(H\), and \(M\) are collinear.
• Question 4: A clockwise rotation of \(68^{\circ}\) about point \(C\) is equivalent to a counter - clockwise rotation of \(360^{\circ}-68^{\circ}=292^{\circ}\) about point \(C\)

Answer:

• Question 2: 1. they are the same length
• Question 3: 3. \(G\), \(H\), and \(M\) are collinear
• Question 4: 4. a rotation of \(292^{\circ}\)