Vocabulary
A transformation of a figure that flips the figure across a line
Reflection
What is the coordinate of the point (2, 5) that is translated 3 units left.
(5,5)
When I reflect over the x-axis which coordinate stays the same?
The x coordinate
(x,y)-->(x,-y)
This angle of rotation creates the same image if it's rotated clockwise or counterclockwise.
180 degree rotation
Enlargement or Reduction: Dilation by a scale factor of 4/3.
Enlargement
A transformation in which a geometric figure slides along a straight line to another location without any change in size or orientation.
Translation
Find the coordinates of A' if A(2, 4) is translated by (x+2, y-5).
A'(4, -1)
Reflection over the y-axis: (x,y) --> (___, ___)
(x, y) --> (-x, y)
The rotation that creates the same image as a rotation 270 degrees clockwise.
90 degrees counterclockwise
Determine the scale factor:
B(2, 5) and B'(1, 2.5).
1/2
Operations that alter the form of a figure. Examples: translations, reflections, dilations, and rotations.
Transformations
Triangle XYZ has coordinates X(0,3), Y(3, -2), and Z(4,0). Find the coordinates of Z'when the figure is translated 3 units to the left and 5 units up.
Z'(1, 5)
The endpoints of a line segment has the coordinates X(-3, 1) and Y(-1, 4). Find the coordinates of X' when X is reflected over the x-axis.
X'(-3, -1)
The coordinate mapping for a rotation clockwise of 90 degrees.
(x, y) --> (y, -x)
A figure has coordinates X(12, 4), Y(8, 2) and Z(-4, 0).What are the coordinates of Y' when dilated by a scale factor of 2/4.
Y'(4, 1)
A transformation in which a plane figure turns around a fixed center point.
Rotation
Find the coordinates of X', Y', and Z' when triangle XYZ with coordinates X(0,3), Y(3, -2), and Z(4,0) is translated using this rule (x-5, y+1).
X'(-5, 4) Y'(-2, -1)
Z'(-1, 1)
Reflect x(3, -5) over x-axis. What are the new coordinates? What if it was over the y- axis instead?
X axis (3, 5)
Y axis (-3, -5)
This angle of rotation maps (x, y) --> (-y, x).
270 degrees clockwise or 90 degrees counterclockwise
Find the coordinates of X' Y' and Z' when X(12, 4), Y(8, 2) and Z(-4, 0) are dilated by a scale factor of 1/4.
X'(3, 1) Y'(2, 1/2)
Z'(-1, 0)
A transformations that preserves distance; e.g. reflection, rotation, and translation.
Rigid Transformation
The coordinate mapping when D(-5, 4), E(-4, 1), and F(-2, 1) are translated to D'(-5,0), E'(-4, -3), and F'(-2, -3).
(x, y)-->(x, y-4)
Triangle MNO has coordinates M(-2, -4), N(-3, 1), and O(4, 2). Find the new coordinates of the triangle when it is reflected over the y axis.
M(2, -4) N (3, 1)
O(-4, 2)
Find the coordinates of A' and B' when A(-3, -2) and B(-1, 2) are rotated clockwise 180 degrees.
A'(3, 2) and B'(1, -2)
A figure has the coordinates A(3, 0), B(5, 5), and C(2, 4). Find the coordinates of the image when dilated using the scale factor 3/2.
A'(4.5, 0) B'(7.5, 7.5)
C'(3,6)