Translations
Describe the translation
A(-4,5) --> A'(1,3)
Right 5 down 2
Reflect point A(2,3) over the y-axis to determine the cooridnate of A'
A'(-2,3)
Rotating a shape 90 degrees clockwise is the same as rotating the shape ____ degrees counterclockwise.
270 degrees
X(3,6) Y(-1,2) Z(-4,-1)
X'(-3,6) Y'(1,2) Z(4,-1)
Reflection over the y-axis
Two parallel lines have the ________ slope and two perpendicular lines have ________ _________ slopes.
same
negative reciprocal / opposite reciprocal
Move point B(1,3) left 4 and up 6 to get B'. What are the coordinates of B'
B'(-3,9)
Reflect point B(-3,1) over the y-axis to get the coordinate of B'
B'(3,1)
Use the coordinate rule (x,y) -> (y,-x) to roatate point A(-3,-7) 90 degrees clockwise.
A'(-7,3)
Draw the line x = -3 (or describe how you would draw the line x = -3)
Vertical line that goes through -3 on the x-axis
what is the segment addition postulate?
the parts of the segment added together equal the total segment
Write the coordinate rule for a transformation left 4 and up 2.
(x,y) --> (x-4,y+2)
Reflect the point X(-4,-2) over the line y=x to get the coordinate of X'
X'(-2,-4)
Use the coordinate rule (x,y) -> (-x,-y) to roatate point L(0,5) 180 degrees.
L'(0,-5)
Draw the line y = -x (or describe how you would draw the line y = -x)
The diagonal line that goes through every point where y = -x (-3,3) (-2,2) (0,0) (1,-1).
A diagonal line that goes through (0,0) and has a slope of negative 1
What is a ray?
A ray is a line that goes indefinitely in one direction
Describe the coordinate rule in words
(x,y) --> (x,y-4)
Down 4
Reflect point R(3,-4) over the line y=-x to get the coordinate of R'
R'(4,-3)
Write the coordinate rule for the following rotation.
M(6,-4) --> M'(4,6)
(x,y) --> (-y,x)
What kind of transformation occurred?
L(-1,3) M(0,-2) N(4,3) O(6,-2)
L'(1,-3) M'(0,2) N'(-4,-3) O'(-6,2)
Rotation 180 degrees
Points that fall on the same plane
Triangle ABC has vertices A(0,0) B(4,2) (2,6).
Come up with a translation that would move triangle ABC to the 3rd quadrent. Hint quadrent three is the bottom left corner where x and y are negative.
Answers will vary,
Reflect P(-2,5) over the line x = -3 to get the coordinate of P'
P'(-4,5)
How many degrees counterclockwise was point Z rotated?
Z(2,8) --> (8,-2)
270 degrees
Reflect point P(4,5) over the x-axis and then translate it (x-3,y-2).
P'(4,-5)
P''(1,-7)
Define
- vertical angles
- linear pair
- adjacent angles
- complementary angles
vertical angles - opposite angles that are the same measure
linear pair - two adjacent supplementary angles
adjacent angles - two angles that share a vertex and a common side
complementary angles - two angles that sum to 90 degrees