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