A translation is when you do what to a figure?
Reflect it over two parallel lines.
A reflection is when you do what to a figure?
Make a transformation such that each preimage point is equidistant across a reflection line from the image point
and
that each pair of pre-image, image points makes a line segment perpendicular to the reflection line
A rotation is when you do what to a figure?
Reflect it over two intersecting lines.
A combination between a reflection and translation.
Glide Reflection
What are three types of isometries?
1 reflection, 2 reflections, 3 transformations
Find the new coordinates of (10,12) if you translate the point three units left and 4 units up.
(7,16)
What does the Reflection Postulate say?
IF its a reflection
THEN 1:1, collinearity, betweenness, distance, angle measure are preserved AND orientation is reversed
After you rotate the point (5,4) 180º clockwise, which quadrant would the point be in?
Quadrant III
Identify the transformation shown.
Rotation OR Two reflections across intersecting lines.
BONUS 100 points: How many degrees was this object rotated?
Define the word transformation
a 1 : 1 correspondence of points between a preimage and an image
Write the formula notation of point (x,y) after it moves 3 spots to the left and 7 spots up.
(x-3,y+7)
Give the coordinates of point (5, -2) after it is reflected over the y-axis.
(-5, -2)
How many degrees rotation from blue to green?
180 Degrees
If I wanted to reflect triangle ABC over the line m and then reflect triangle A'B'C' over the line h, how would I write out the transformation leading to A"B"C"?
A"B"C" = (give a complete description of the letters and symbols needed to write out the abbreviation for this transformation)
A"B"C" = Rh o Rm (ABC)
What is the type of transformation that produces congruent figures.
Isometry
What is the translation vector?
or (-4, -4)
Give the coordinates of point (x,y) after it is reflected over the x-axis.
(x,-y)
If the magnitude of rotation between green and blue is 90 degrees, what is the magnitude of the acute angle between the two lines?
The acute angle is 45 degrees
What does the Two Reflection Theorem for Translations say?
Figure distance = (2) parallel line distance
What are the two categories of congruent?
Direct and Opposite
∆LMN is translated 6 units to the right and 4 units down. L(0,3) M(6,4) N(3,9)
What are the coordinates for L' M' and N'?
L'(6,-1), M'(12,0), N'(9,5)?
Give the name of the conditional statement below.
IF a figure is made up of points
THEN the reflection image is made up of reflected images of each of those points
Figure Reflection Theorem
Give the full name for the following conditional statement.
IF its a rotation
THEN the angle of rotation between the figures is twice the acute angle measure between the lines.
Two Reflection Theorem for Rotations
What is point D (-6,2) after being reflected over the line x=1 and then translated down 3.
(8,-1)
Name one of each: linear pair, vertical angles, corresponding angles, adjacent angles
linear pair: 1,5 or 6,7 or 9,8
Vertical angles: 6,8 or 9,7
Corresponding angles: assuming lines are parallel! 1,6 or 5,7 or 8,4
Adjacent angles: 1,2 or 2,3 or 3,4 or 4,5 or 5,1 or 6,9 or 9,8 or 8,7 or 7,6