Question

for items 7 - 10, use the figure shown. find the coordinates of the specified vertex after the given sequence of transformations.

1. a reflection across ( y = 0 ), then a translation 1 unit left and 2 units up

( s: square, square )

1. a rotation ( 90^{circ} ) about the origin, then a reflection across ( x = 0 )

( r: square, square )

1. a rotation ( 90^{circ} ) about the origin, then a reflection across ( x = 0 )

( t: square, square )

1. a translation 2 units right, then a reflection across ( x = 0 )

( q: square, square )

1. what type of symmetry does a rectangle have?

(a) reflectional but not rotational symmetry.
(b) rotational but not reflectional symmetry.
(c) both reflectional and rotational symmetry.
(d) a rectangle is not symmetric.

1. if a figure is translated 3 units left and 3 units up which translation moves the image back to the original position?

(a) 3 units right and 3 units down
(b) 3 units left and 3 units up
(c) 3 units up
(d) 3 units left

1. given the regular polygon, select all of the rotations and reflections that carry the figure onto itself.

□ a. a rotation of ( 72^{circ} ) around the center, point d
□ b. a reflection across line a, through two vertices
□ c. a reflection across line b, through one vertex, the center d
□ d. a rotation of ( 60^{circ} ) around the center, point d
□ e. a reflection across line c, and the midpoint of the opposite side

1. for a rotation ( x^{circ} ) about point p, which of the following is not true?

(a) for a preimage point a,( m angle a p a^{prime}=x ).
(b) the transformation rotates every point in the preimage ( x^{circ} ) about point p.
(c) for a preimage point a,( p a = p a^{prime} ).
(d) for any polygon, the rotation can be expressed as a single reflection no matter what the value of ( x ) is.

1. point ( p(-6,-4) ) is the image of point ( p(-2,3) ) under a translation. what is the image of ( (5,-1) ) under the same translation?

(a) ( (9,6) )
(b) ( (1,-8) )
(c) ( (-1,-5) )
(d) ( (3,2) )

Explanation:

Question 11

A rectangle has two lines of reflectional symmetry (the lines connecting the mid - points of opposite sides). A rectangle also has rotational symmetry of order 2 (a rotation of \(180^{\circ}\) about its center maps the rectangle onto itself).

If a figure is translated \(a\) units left and \(b\) units up, to get back to the original position, we need to translate \(a\) units right and \(b\) units down. Here \(a = 3\) and \(b=3\).

• For a rotation of \(x^{\circ}\) about point \(P\):
• The measure of the angle between a pre - image point \(A\) and its image \(A'\) with respect to the center of rotation \(P\) is \(m\angle APA'=x\) (by the definition of rotation).
• A rotation is a transformation that rotates every point in the pre - image \(x^{\circ}\) about point \(P\).
• A rotation is an isometry, so \(PA = PA'\).
• A rotation (except for \(180^{\circ}\) rotation in some cases) cannot be expressed as a single reflection. A rotation of \(x^{\circ}\) (\(x

eq180\)) about a point \(P\) is a different transformation from a reflection.

Answer:

C. Both reflectional and rotational symmetry.

Question 12