A plane has this if it can be mapped onto itself by a reflection in a line.
What is a line of symmetry
100
This is the fixed point in which a figure is rotated around.
What is the center of rotation
100
This is a quanity that has both direction and magnitude. Represented by an arrow drawn between two points.
What is a vector
100
This is a transformation that consists of 2 or more transformations performed one after the other.
What is a composition
100
Game designers use this type of transformation most so that they don't have to re-create the character every time it moves.
What is translation
200
This is a transformation that preserves angle measures, lengths, lines, and distances.
What is isometry
200
Does a regular octagon have rotational symmetry? If so, describe the rotations that map the figure onto itself.
Yes, it has rotational symmetry. It can be mapped onto itself by a clockwise or counterclockwise rotation of 45°, 90°, 135°, or 180° about its center.
200
If point P is on (0,0) and point Q is on (5,3), how do you write the component form of (arrow on top)PQ.
<5,3>
200
the first translation maps J to J' and the second maps J' to J". Find the translation that maps J to J".
Translation 1: (x, y) --> (x+7, y-2)
Translation 2: (x, y) --> (x-1, y+3)
Translation: (x, y) --> (????? ?, ?????)
(x, y) --> (x+6, y+1)
200
This is an artist who uses rotational symmetry which we looked at in class.
What is M. C. Escher
300
If N(2, 4) is reflected in the line y = 2, then what is N'?
(2, 0)
300
What are the coordinates of A' B' and C' when triangle ABC is rotated 90 degrees clockwise about the origin. A = (-1,1), B = (2,4), and C = (2, -5).
A' = (1, 1)
B' = (4, -2)
C' = (-5, -2)
300
in (arrow on top)AB, the point A is the _______ point and point B is the ________ point. (Vocabulary words)
A is the initial point and B is the terminal point.
300
What are the coordinates of P'', Q'', and R'' after this composition?
P(5, 1), Q(3, 4), R(0, 1)
Translation: (x, y) --> (x - 2, y - 4)
Reflection: in the y-axis
P''=(-3,-3)
Q''=(-1,0)
R''=(2,-3)
300
Basic geometry is used in what career for finding out how much in supplies (fencing, carpet, concrete or other material) is needed to cover a specific area?
What is a carpenter
400
Two houses are located on a rural road m. You want to place a telephone pole on the road at point C so that the length of the telephone cable, AC + BC, is a minimum. One house is point A and the other is point B.
Where should you locate C? (Explain steps to find it)
Reflect A in line m to obtain A'. Then, draw line A'B.
Label the point at which this segment intersects
m as C. Because line A'B represents the shortest
distance between A' and B, and AC = A'C, you
can conclude that at point C a minimum length
of telephone cable is used.
400
Lines m and n intersect at point D. Consider a reflection of triangle ABC in line m followed by a reflection in line n. What is the measure of the acute angle between lines m and n, when the angle of rotation about D is 162°?
81 degrees
400
(Arrow on top) PQ = <4,1>
A (-1, w), A' (2x + 1, 4)
B (8y - 1, 1), B' (3, 3z)
w=?
x=?
y=?
z=?
w=3
x=1
y=0
z=2/3
400
Describe the composition of the transformations.
There are 3 lines, line PQ, line P'Q', and line P"Q".
P=(-1,1) Q=(-1,5)
P'=(1,1) Q'=(5,1)
P"=(1,-2) Q"=(5,-2)
line PQ is rotated 90 degrees clockwise about the origin and then reflected over x=-.5
400
Everybody in the world owns this. This uses rotation, reflection, translation, and dilation but usually not all together.
What are clothes. Even clothes are stitched using geometrical measurements as they have to take a 3 dimensional shape but are made from flat 2 dimensional cloth.
500
What is the value of x in triangle ABC if the angle measure of B is 5x, A is 2x and C is 2x?
x = 20 degrees
500
This 4-sided geometric shape doesn't have rotational symmetry unlike a square or rectangle.
What is a trapezoid.
500
First team to make a valid, sensible word problem with an answer about translations or vectors gets 500 points! All teams can answer!
Yay! Whichever team wrote a word problem and answer first gets to choose the next one!
500
This popular computer game uses pentominoes to score points.
What is Tetris
500
How do radiographers use transformations in their career? And which transformation do they mostly use?
They use modern computerized medical equipment for imaging, often use dilation to determine the size of tumors in a CAT scan, the size of an unborn baby during an ultrasound or the size of a bone fracture in an x-ray.