Reflections

Reflections
Translations Battleship Warm Up
Phase 1: Position your battleships on your gameboard according to the following specifications: -‐ Aircraft Carrier -‐ rectangle, area of 5 units2, 2nd quadrant only -‐ Battleship -‐ square, area of 4 units2, both 1st and 4th quadrant -‐ Submarine -‐ parallelogram area of 3 units2, 3rd quadrant -‐ Destroyer -‐ trapezoid, area of 2 units2, you choose the quadrant Phase 2: Write the coordinates of each battleship in both your gameboard AND your opponent’s gameboard. Phase 3: The enemy is getting closer. Time to move. You must move all of your boats at least once. Write all as Translation Rules using the correct notation. Redraw your moved boats in another color on your board! Write the rules in your board area and your opponent's. Example of Translation Rule: Aircraft carrier (x, y) (x -‐ 2, y + 3) Phase 4: Hand your answer key to Ms. Hahn and then switch with your opponent gameboards with your partner. Work to find each other’s boat locations after the translations. Check your game board with me when you think you sunk all their ships. First person to find each other’s ships wins! Your gameboard will be graded as an assignment grade! If you win your duo, you’ll win a prize! Reflections in the Coordinate Plane
A reflection is a transformation which ____________ the figure over a ________________________. This line is called the . EXAMPLE 1
ΔABC is being reflected over the x-‐axis. Draw and label the image ΔA’B’C’. We can use an arrow to describe this reflection. ΔABC à ΔA’B’C’ What are the coordinates of: A ________ à A’ _________ B ________ à B’ _________ C ________ à C’__________ Write a general rule for an x-‐axis reflection: (x, y) à ( ________ , _______ ). EXAMPLE 2 ΔABC is reflected over the y-‐axis. Draw the image ΔA’B’C’. What are the coordinates of: A ________ à A’ _________ B ________ à B’ _________ C ________ à C’ __________ Write a general rule for a y-‐axis reflection: (x, y) à ( ________ , _______ ). Tell me more about the relationship between the preimage and the image. Are they congruent or similar? Explain how you know. EXAMPLE 3 a) Draw ΔABC which has coordinates A(1, 0), B(5, -‐2), and C(3, -‐3). y
8
7
b) Draw the image ΔA’B’C’ after a reflection of 6
ΔABC over y = x . 5
4
3
c) List the coordinates of A’B’C’. 2
1
A (1, 0) à A’ _________ –8
–7
–6
–5
–4
–3
–2
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
x
–2
B (5, -‐2) à B’ _________ –3
–4
–5
C (3, -‐3) à –1
–1
C’__________ –6
–7
Write a general rule for an y = x reflection: –8
(x, y) à ( ________ , _______ ). EXAMPLE 4
a) Draw ΔABC which has coordinates A(0,1), B(3,4), and C(5,1). y
b) Draw the image ΔA’B’C’ after a reflection of ΔABC over y = -‐x. 8
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c) List the coordinates of A’B’C’. 6
5
4
A (0, 1) à A’ _________ 3
2
1
B (3, 4) à B’ _________ –8
–7
–6
–5
–4
–2
–1
–1
–2
C (5, 1) à –3
C’__________ –3
–4
–5
–6
–7
Write a general rule for an y = -‐x reflection: (x, y) à ( ________ , _______ ). –8
EXAMPLE 5
a) Draw ΔABC which has coordinates A(-‐3, 1), B(1, 5), and C(4, 2). b) Draw the image ΔA’B’C’ after a reflection of ΔABC over y = 2. y
8
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c) List the coordinates of A’B’C’. 6
5
A (-‐3, -‐1) à 4
A’ _________ 3
2
1
B (1, 5) à B’ _________ –8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
x
5
x
–2
C (4, 2) à C’__________ –3
–4
–5
–6
–7
–8
*** You can reflect over any line, but the most important ones are listed as follows: Reflection Line Rule x-‐axis y-‐axis y = x y = -‐x Reflections Practice
1. Draw the line of reflection which caused rectangle KLMN to reflect onto rectangle K’L’M’N’. What is the equation of the line of reflection? y
5
4
3
2
1
L
–5
–4
–3
K K'
–2
–1
–1
L'
1
2
3
4
–2
–3
M
–4
N
N'
–5
M'
y
5
2. Draw the line of reflection which caused triangle ABC to reflect 4
onto triangle A’B’C’. What is the equation of the line of reflection? 3
B
2
A
1
–5 –4 –3 –2 –1
1
2
3
–1
–2
A'
–3
–4
B'
–5
y
7
3. Find the reflection of the triangle HOT over the x-‐axis. 6
5
O
4
3
Write the coordinates of H’O’T’. 2
1
H
–7 –6 –5 –4 –3 –2 –1
1
2
3
4
–1
–2
Is the image similar or congruent? How do you know? –3
–4
–5
–6
–7
4. Find the reflection of the quadrilateral WXYZ across the dotted line. What is the equation of the dotted line? y
8
7
6
5
4
Label the image W’ X’ Y’ Z’. 3
X
2
1
W
–8 –7 –6 –5 –4 –3 –2 –1
1
2
3
4
5
–1
Y
–2
–3
Z
–4
–5
–6
–7
–8
C
4
5
x
C'
T
5
6
7 x
6
7
8 x
5. Quadrilateral CDEF is plotted on the grid below. On the graph, draw the reflection of polygon CDEF over the line y = x. Label the image C’D’E’F’. Now create polygon C”D”E”F” by translating polygon C’D’E’F’ three units to the left and up two units. What will be the coordinates of point C”? Answer ______________ 6. a) Draw ΔJKL which has coordinates J (0,2), K (3,4), and L (5,1). b) Draw the image ΔJ’K’L’ after a reflection of ΔJKL over the x-‐axis. y
c) List the coordinates of J’K’L’. J (0, 2) à 8
7
J’ _________ 6
5
K (3, 4) à 4
K’ _________ 3
2
L (5, 1) à d) Draw the image ΔJ’’K’’L’’ after a reflection of ΔJ’K’L’ over the y-‐axis. e) List the coordinates of J’’K’’L’’. J’_________ à 1
L’__________ J’’ _________ –8
–7
–6
–5
–4
–3
–2
–1
–1
1
–2
–3
–4
–5
–6
–7
–8
K’_________ à K’’ _________ L’_________ à L’’__________ f) Describe a different combination of two reflections that would move ΔJKL to ΔJ’’K’’L’’. g) Is this new image congruent or similar to the original figure? 2
3
4
5
6
7
8
x

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