Translations
What is a translation in geometry?
A figure that moves in the same direction and the same distance on a coordinate plane.
What is a rotation in geometry?
When a figure turns around a center of rotation.
What is a reflection in geometry?
A figure that flips over a line of reflection.
What is a sequence of transformations?
When more than one transformtion is performed to change the orientation of a shape in the coordinate plane.
How do you translate a point A(2, 3) by 3 units to the right and 2 units down?
(2, 3) --> (x + 3, y - 2)
Define the center of rotation.
The point in the middle of a rotation.
What are the properties of a shape after it is reflected over the x-axis?
The same side lengths and same angles.
List the types of transformations that can be combined in a sequence.
Translation, Reflection, Rotation
Describe the effect of translating a shape on its size and orientation.
The size doesn't change. The orientation does change.
If a point B(4, 2) is rotated 900 clockwise about the origin, what are the new coordinates?
2, -4
If point C(3, 4) is reflected over the y - axis, what are the new coordinates?
(-3,4)
What happens to the cooridinates of a rotation that is 1800 in either direction?
The cooridinates of a rotation of 1800 become the opposite of the original (x,y) --> (-x,-y).
If a triangle has vertices at A(1, 1), B(2, 3), and C(3, 1), what are the new coordinates after a translation of (x + 4, y - 2)?
A (5, -1) B (6, 1) C (7, -1)
How does the angle of rotation affect the position of a shape?
The angle of rotation determines which direction a figure is rotated.
How do reflections affect the orientation of a shape?
A reflection changes the shapes orientation by flipping the shape over a line of reflection.
If a square is first translated 2 units right and then rotated 900 clockwise, what is the final position of a vertex originally at D(1, 1)?
D' (1,1) --> (3,1) --> (1, -3)
Explain how to write the rule when doing a translation.
(x, y) --> x -- add to go right subtract to go left / y -- add to go up subtract to go down
Rotate a triangle with vertices at A(0, 0), B(0, 2), and C(2, 0) by 1800 around the origin. What are the coordinates.
A (0, 0) B (0, -2) C (-2, 0)
Describe the process of reflecting a triangle over the y-axis.
A triangle reverses its direction of orientation. The x in the coordinates of its verticies become the opposite sign of its original verticies.
If a triangle is first translated 3 units left, 2 units up and then rotated 900 counterclockwise, what is the final position of a vertex originally at C(-2,1)?
C'' = (-2,1) ---> (-5, 3) ---> (-3, -5)