1. Unit 1: Transformations Day 3: Reflections Honors

2. Warm Up #
1. Suppose a translation slides the point X(-3, 4) to the point X’(-1, 1). Write a rule (x, y)  ( ___ , ___ ) that describes this translation. 2. The points A(2, 7) and B(-5, 4) are translated by the vector <-4, 1>. Determine the coordinates of the image points A’ and B’
Have Homework and Signed Syllabus out!!!

3. Essential Question #3
How can coordinates be used to describe reflections?

4. Intro Draw a picture of what you think a reflection looks like.
Some things to think about:
When/Where can you see a reflection?
What does your reflection look like?

5. Do we see a reflection?
What is that black line at sea level? What do you notice about the mountain and its reflection? What about the points on the black line? Are they reflected anywhere?
Want students to see that every point of the actual mountain(preimage) is exactly the same distance from the black line as its corresponding point in the reflected mountain(image).

6. Reflection
Definition: A Reflection is a transformation in which the preimage is flipped across a line of symmetry.

7. Line of Symmetry
The Line of Symmetry is the line that the preimage is reflected over.
When you connect the preimage and image with a line segment, the Line of Symmetry will be the Perpendicular Bisector of the segment

8. Group Work
Just like with translations, line reflections can be expressed using coordinates. In this investigation, you will build coordinate models for reflections across vertical and horizontal lines, as well as across the lines y = x and y = -x.
Take 15 minutes to complete pages 4a & 4b in your packet!

9. Reflections across the lines y = x and y = -x
15 minutes to complete pages 4c – 4d in packet
y = -x has
slope = -1
y-intercept = 0
y = x has
slope = 1
y-intercept = 0

10. General Rules for Line Reflections
Reflection across
The x-axis :
The y-axis :
The line y = x :
The line y = -x :

11. Example M (-1, 5) W (-1, 4) A (4, 3) D (1, 5)
Write the rule and graph the image
M (-1, 5)
W (-1, 4)
A (4, 3)
D (1, 5)

12. Reflection over other lines
Remember! You can reflect across ANY line by thinking about the perpendicular bisector!
I (-3, -2)
E (-3, -3)
X (0, -5)
Q (2, -4)

13. What if I can’t remember the rules?
Take a piece of graph paper. Place a coordinate like (1,2) in quadrant 1. Fold the graph paper along your line of reflection. The new point will provide you with your rule for the 4 rules we have.

14. Homework
Homework: Pages 5-6 in packet