Transformations, Sequences, and Congruence

Congruence Transformations

Geometry

Mrs. LaGrange

Warm up!

Do you remember?

Multiple Choice

Use the distance formula

$$\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$$  to find the length of  $$\overline{AB}$$  for  A(2,7) and B(7,-5).

• 169

• 13

• 85

• $$\sqrt{17}$$  

Multiple Choice

What point is 6 units to the right of (3,5)?

• (3, 11)

• (9, 11)

• (9, 5)

• (3, 11)

Multiple Choice

Are these triangles congruent?

• Yes

• No

Math spoken here.

Vocabulary

Transformation: the change

Preimage: original

Image: new

Identify Transformations

Reflection: uses a line of reflection to create a mirror image of the original feature.

Reflection Reference Guide:

Coordinate notation

Multiple Choice

Which graph shows the pre-image reflected over y-axis?

Multiple Choice

Identify the transformation from ABC to A'B'C'.

• 90^o clockwise rotation
• 90^o counter clockwise rotation
• Reflection across the y-axis
• Reflection across the x-axis

Multiple Choice

What is a reflection?

• When you turn an object around a point.
• When you slide an object form one place to another.
• When you flip or mirror an object across a line.
• When you resize an object.

Multiple Choice

Is the picture being reflected in the y-axis or x-axis?

• y-axis
• x-axis

Multiple Choice

Which answer shows a reflection across the x-axis?

• d
• c
• b
• a

Multiple Choice

Flipping a figure is a ...

• Rotation

• Reflection

• Dilation

• Translation

Rotation about a point

Rotation is the turning or spinning of a figure through a specific angle and direction about a fixed point.

Note: Point A is called the center of rotation or turn center.

Rotation Quick Reference

Coordinate Plane (In this lesson if a rotation is shown in a coordinate plane the center of rotation is the origin.)

Rotations: Direction and Angle

The direction of a rotation can be clockwise or counterclockwise. The angle of rotation is formed by rays drawn from the center of rotation through corresponding points on the original figure and its image.

Multiple Choice

What is the angle of rotation for this counterclockwise rotation about the origin?

• 90°
• 180°
• 270°
• 360°

Multiple Choice

How many degrees was the figure rotated?

• 90 degrees counterclockwise 
• 180 degrees
• 270 counterclockwise 
• 90 degrees clockwise

Multiple Choice

Triangle C is rotated 180° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A
• B
• C
• D

Multiple Choice

What is this picture an example of? 

• An angle
• A cat vertex 
• Rotation 
• Dilation

Translations:

In the coordinate plane, a translation moves an object a given distance right or left and up or down.

Multiple Choice

How is trapezoid ABCD translated to trapezoid A'B'C'D'?

• Translated 5 units down and 5 units to the right
• Translated 5 units down and 1 to the right
• Translated 8 units down and 5 units to the right
• Translated 5 units down and 4 units to the right

Multiple Choice

How was B translated to B' if B' is at (4, -2)?

• Translated 6 units down
• Translated 2 units to the left and 6 units down
• Translated 2 units to the right and 6 units down
• Translated 2 units to the right

Multiple Choice

Determine where T' would be if you translated T 3 units to the right and 6 units up.

• (5, 1)
• (2, -5)
• (-1, 1)
• (8, -2)

Multiple Choice

Determine how to translate triangle A'B'C' to triangle ABC.

• (x+2, y-5)
• (x+2, y-9)
• (x-2, y-9)

Questions?

Your turn for practice.