Transformations

What is our TEKS?

TEKS 8.10C:

The student will explain the effect of reflections over the x‐ or y‐axis as applied to two‐dimensional shapes on a coordinate plane using an algebraic representation.

Reflections, TEKS 8.10C (R)

It's time for our lesson . . .

​Reflections

You should take notes in a piece of the information presented in the video and slide. Please make sure you are reading.

Open Ended

What is one thing that you learned from the video?

Reflections:

• Represents the flipping of an image

• When an object is reflected, the pre-image and image are always congruent (SAME SIZE AND SAME SHAPE).

• Each point in the image and pre-image is the same distance from the line of reflection. (They are mirror images of each other.)

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.

Open Ended

Where do we see reflections in the real world?

Multiple Choice

When a figure is reflected over a line of reflection, the new image is congruent to the original. True or False

• True

• False

Multiple Choice

True or false: When a point is reflected across a line of symmetry, it remains the same distance from the line.

• true

• false

Line of Reflection:

• The line of reflection is the axis that the point or figure is being reflected across.

• It is also known as the line of symmetry.

Multiple Choice

Identify line of reflection.

• x axis

• y axis

• y = x

• y = -x

Multiple Choice

What axis is the triangle being reflected over?

• X-axis

• Y-axis

Reflections across the y-axis:

• (x, y) --> (-x, y)

• The y coordinate stays the same.

• The x coordinate changes sign.

• A(-8, 7) --> A'(8, 7)

Multiple Choice

Which answer shows a reflection across the y-axis?

• a

• b

• c

• d

Reflections over the x axis:

• (x, y) --> (x, -y)

• The x coordinate stays the same.

• The y coordinate changes sign.

• A(-8, 7) --> A'(-8, -7)

Multiple Choice

Which answer shows a reflection across the x-axis?

• d

• c

• b

• a

​Reflection Rules:

• ​Over the x-axis:  (x, -y) means keep the sign of x and change the sign of y.

 

• Over the y-axis: (-x, y) means keep the sign of y and change the sign of x.

​I would copy this slide

This sequence of problems are meant for you to learn how to answer these questions.

Time for Guided Practice . . .

Reflections, TEKS 8.10C (R)

Multiple Choice

How do you represent reflection over the x axis algebraically?

What is the rule?

• (-y, -x)

• (x + a, y + b)

• (x , -y)

• (-x, y)

Multiple Choice

Find K' if the figure is reflected across the x-axis

(use the rule)

• (4, 1)

• (-1, -4)

• (1, -4)

• (1, 4)

Multiple Choice

What is the image of S(2,-8), after a reflection over the line x axis?

(use the rule)

• S'(-2,-8)

• S'(2, 8)

• S'(-8,2)

• S'(8,-2)

Multiple Select

Select all the sets that are reflections across the X AXIS.

(use the rule)

• A(5, 6) --> A'(5, -6)

• B(3, -8) --> B'(3, 8)

• C(5, -5) --> C'(-5, -5)

• D(-6, -1) --> D'(-6, 10

• E(1, 6) --> E'(1, -6)

Multiple Choice

What is the image of Z(-1, 4) after a reflection over the y axis?

(use the rule)

• Z'(4, -1)

• Z'(-1,-4)

• Z'(4, 1)

• Z'(1, 4)

​​Even though is independent practice that doesn't mean you do it by yourself. Ask your community for help if you need it.

Time for Independent Practice . . .

Reflections, TEKS 8.10C (R)

Multiple Choice

Identify line of reflection.

• x axis

• y axis

• y = x

• y = -x

Multiple Choice

What is this transformation?

(x, y) ----> (-x, y)

• Reflect over the x axis

• Reflect over the y-axis

• Slide down 1

• slide left 1

Multiple Choice

Reflect Point C over the y-axis:

• (-3, 2)

• (3,2)

• (-2,3)

• (3,0)

Multiple Choice

Reflect Point C over the y-axis:

• (-3, 2)

• (3,2)

• (-2,3)

• (3,0)

Multiple Choice

Reflect over x-axis. Which point would be at (3, -6)

• A

• B

• C

• H

Multiple Choice

What is the Algebraic Notation for this Reflection?

• (x, y) → (y, x)

• (x, y) → (-x, y)

• (x, y) → (-y, -x)

• (x, y) → (x, -y)

Multiple Choice

Where will A' be at, if triangle ABC is reflected across the y-axis using the rule: (x, y) --> (-x, y)?

• (2, 1)

• (1, -2)

• (-1, 2)

• (-2, 1)

Multiple Choice

Triangle GHI is reflected across the x-axis.  What are the coordinates of I'?

• (-2, 6)

• (2, 6)

• (-6, -2)

• (6, 2)

Multiple Choice

∆BCD contains the points: B(2,3) C(2,1) D(5,1). If the triangle is reflected across the x-axis, what will B' be?

• B'(2, -3)

• B'(-2, 3)

• B'(-2, -3)

• B'(2, 3)

Multiple Choice

Point C (-5, 4)

Reflect over the x-axis.

What is C'?

• (5, 4)

• (-5, -4)

• (5, -4)

• (-5, 4)

Time for your Mastery Check:

It's time to assess your skills using a STAAR-related problem. Carefully select your answer to the next problem to test your knowledge. You will use this for your Self-Assessment.

Reflections, TEKS 8.10C (R)

Multiple Choice

What is the Algebraic Notation for this Reflection?

• (x, y) → (y, x)

• (x, y) → (-x, y)

• (x, y) → (-y, -x)

• (x, y) → (x, -y)

Poll

Self-Assessment:

• I'm an expert. I got this! (I can teach this skill to others.)

• I'm a Practitioner. I can do this with more practice. (I can re-do this lesson through Google Classroom.)

• I'm a Novice. I need help learning this skill! (I can come to tutoring to get the help I need, or I can ask an Expert for help.)