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,
( mangle apa = x ).
(b) the transformation rotates
every point in the preimage ( x^{circ} )
about point p.
(c) for a preimage point a,
( pa = pa ).
(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:

Step1: Determine the translation rule

The translation from \(P(-2,3)\) to \(P'(-6,-4)\) has a horizontal change \(x\) - coordinate: \(-6-(-2)=-4\) and a vertical change \(y\) - coordinate: \(-4 - 3=-7\). So the translation rule is \((x,y)\to(x - 4,y-7)\)

Step2: Apply the translation rule to the point \((5,-1)\)

For the \(x\) - coordinate: \(5-4 = 1\)
For the \(y\) - coordinate: \(-1-7=-8\)

Answer:

B. \((1,-8)\)