4.1 Reflections
Determine the coordinates of the image
DEFG
x = -1
D ( 0 , -3 )
E ( 1 , 3 )
F ( 3 , 3 )
G ( 4 , -3 )
D' ( -2 , -3 )
E' ( -3 , 3 )
F' ( -5 , 3 )
G' ( -6 , -3 )
Determine whether a translation maps triangle JKL onto triangle J'K'L'. If so, find the translation vector.
SHOW PICTURE!!!!!!!!
( 2 , 5 )
Triangle XYZ has vertices of X ( 0 , 2 ) , Y ( 4 , 4 ) and Z ( 3 , -1 ). Find the new coordinates after a rotation of 180 degrees about ( 2 , -3 ).
X' ( 4 , -8 )
Y' ( 0 , -10 )
Z' ( 1 , -5 )
Triangle PQR has vertices P ( 1 , 1 ) Q ( 2 , 5 ) and R ( 4 , 2 ). Determine the coordinates of the vertices of the image AFTER a translation along ( -4 , 0 ) AND a reflection in the x-axis.
Q'' ( -2 , -5 )
R ( 0 , -2 )
Determine whether each regular polygon will tessellate the plane.
Pentagon
no, 108 not a factor of 360
Determine the coordinates of S ( -7 , 1 ) after a reflection in the y = 3
S' ( -7 , 5 )
Line segment AB is at points A (2 , 7 ) and B ( 5 , 9 ). What would A' and B' translation be with a vector of
( -5 , -7 )
A' ( -3 , 0 )
B' ( 0 , 2 )
F' ( -3 , -16 )
G' ( -8 , -12 )
H' ( -5 , -10 )
Triangle RST; R ( 1 , -4 ), S ( 6 , -4 ), T ( 5 , -1 )
Translation: along ( 2 , 0 )
Reflection: in x-axis
R'' ( 3 , 4 )
S'' ( 8 , 4 )
T'' ( 7 , 1 )
Determine whether each regular polygon will tessellate the plane.
Hexagon
Yes, 120 is a factor of 360
Determine the coordinates of W ( -7 , 4 ) after a reflection in the line y = 9.
W' ( -7 , 14 )
Name the image of each point after the given translation
Q ( 4 , -2 ) ; Vector ( -2 , -5 )
Q' ( 2 , -7 )
Point Q with coordinates ( 4 , -7 ) is rotated 270 degrees about ( 5 , 1 ). What are the coordinates of Q'?
Q' ( 13 , 0 )
Line segment WX: W ( -4 , 6 ) and X ( -4 , 1 )
Reflection: in x-axis
Rotation: 90 about origin
W'' ( 6 , -4 )
X'' ( 1 , -4 )
Determine whether a semi-regular uniform can be created from the given shapes, assuming that all sides are 1 unit long. If so, determine the number of each shape needed at each vertex to create the tessellation.
Regular pentagons and squares
no
ABC with vertices A ( -3 , 2 ), B ( -4 ,-1 ), and C ( -6 , -1 )
A' ( 2 , -3 )
B' ( -1 , -4 )
C' ( -1 , -6 )
The image of A ( -3 , -5 ) under a translation is
A' ( 6 , -1 ). Find the image of B ( 3 , -2 ) under the same translation.
Vector ( 9 , 4 )
B' ( 12 , 2 )
The line segment XY with endpoints X ( 3 , 1 ) and Y ( 2 , -2 ) is rotated 90 degrees counter clock wise about ( -6 , 4 ). What are endpoints X' Y'?
X' ( -3 , 13 )
Y' ( 0 , 12 )
Describe a single transformation that maps the pre-image onto the image
1
Determine whether each figure has a line of symmetry. If so, draw the lines of symmetry and state how many lines of symmetry it has.
Show Picture
Yes, 8
Vito is drawing the top view of a square sandbox on a coordinate plane with vertices of A ( 1 ,1 ) , B ( 1 , 6 ) C ( 6 , 6), and D ( 6 , 1 ). Vito reflects the sandbox in the line x = 1.
A' ( 1 , 1 )
B' ( 1 , 6 )
C' ( -4 , 6 )
D' ( -4 , 1 )
Maddy reflects an object in the line y = -1. Then she reflects it in the line y = 1. Describe the translation.
(x , y + 4 )
Under a rotation about the origin, the point A ( 5 , -1 ) is mapped on the point A' ( 1 , 5 ). What is the image of the point B ( -4 , 6 ) under this rotation?
90 degree rotation ( -y , x )
B' ( -6 , -4 )
Is triangle JKL congruent to triangle MNP? If so , what composition of transformation maps triangle JKL onto triangle MNP?
Show picture!!
YES
Translated ( 2, 0 )
Rotated 180 degrees
State the order and the magnitude of symmetry
Rotational symmetry: ???
Order: ??
Magnitude ??
Yes
8
45