Perform Congruence Transformations
Jan 02, 2016
Perform Congruence Transformations
Transformations: when you move or change a geometric figure in some way to produce a new figure. Image is what the new figure is called.
Translation: is when we move every point on the figure, the same distance and direction.Reflection: is when we use a line of reflection to create a mirror image of the original figure.
Rotation: Turns a figure about a fixed point called the center of rotation
Congruence Transformations: changing the position of a figure without changing its size or shape. There are 3 types of transformations.
Coordinate Notation for a translation:(x,y) (x+a, y+b)Which shows that each point (x,y) of the blue figure is translated horizontally a units and vertically b units
a
b
x
y
Multiply the y coordinate by -1
(x,y) (x,-y)
Multiply the x coordinate by -1
(x,y) (-x,y)
Reflection in the x-axis Reflection in the y-axis
y
x
y
x
(x,y)
(x,-y)
(-x,y)(x,y)
90 clockwise Rotation
60 counterclockwise rotation
yy
x x
Figure ABCD has the vertices A(-4, 3), B(-2, 4), C(-1, 1), and D(-3, 1). Sketch ABCD and its image after the translation (x, y) (x+5, y-2).
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
y
Figure WXYZ has the vertices W(-1, 2), X(2, 3), Y(5, 0), and Z(1, -1). Sketch WXYZ and its image after the translation (x, y) (x-1, y+3).
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
y
Use coordinate notation to describe the translation.
5 units right, 3 units up
7 units left, 4 units down