Coordinate Reflections - 2Reflecting over the

y = x and y = -x lines

Homework: Reflections on the Coordinate Plane WS 2

Reflection in the x-axis:   

Reflection in the y-axis:

𝑟 𝑥−𝑎𝑥𝑖𝑠∆ 𝐴𝐵𝐶

𝑟 𝑦−𝑎𝑥𝑖𝑠∆ 𝑋𝑌𝑍

UPDATE: Reflection Notation

The line y=xWhere the x and y coordinates are equal:

(1,1), (5,5), (-3, -3)…

(2, 2)

(-5, -5)(-1, -1)

Reflect across y = x

x,y y,xSwap x and y

Notation:

Rule:

Name the coordinates of the original object:

NI

WW: (9, 8)

I: (9, 3)

N: (1, 1)

I’ W’

N’Name the coordinates of the reflected object:

W’: (8, 9)

I’: (3, 9)

N’: (1, 1)

A point ON the line of

reflection is its own reflection

𝑟 ( 𝑦=𝑥 )∆𝑊𝐼𝑁

A(1, 2) A'(2, 1)

B(3, 5) B'(5, 3)

C(4, –3) C'(–3, 4)

D(2, –5) D'(–5, 2) A'

B'

C'

D'

𝑟 ( 𝑦=𝑥 )𝐴𝐵𝐶𝐷

The line y = -xWhere the x and y coordinates are opposites:

(1,-1), (-5,5), (3, -3)…

(-2, 2)

(4, -4)

Reflect across y = -x

x,y y, x Swap and change both signs

𝑁𝑜𝑡𝑎𝑡𝑖𝑜𝑛 :𝑟 (𝑦=−𝑥)

Rule:

Name the coordinates of the original object:

A: (-4, 6)

B: (-1, 6)

C: (-1, 3)

Name the coordinates of the reflected object:

A’: (-6, 4)

B’: (-6, 1)

C’: (-3, 1)

A’

B’ C’

𝑟 ( 𝑦=−𝑥)∆ 𝐴𝐵𝐶

𝑟 ( 𝑦=−𝑥)∆ 𝐴𝐵𝐶

Name the coordinates of the original object:

A: (1,2)

B: (1,5)

C: (3,2)Name the coordinates of the reflected object:

A’: (-2,-1)

B’: (-5, -1)

C’: (-2, -3)

C’

B’ A’

Reflection in y = x:

Reflection in y = -x:

Reflection Notation

𝑟 ( 𝑦=−𝑥)∆ 𝐴𝐵𝐶

𝑟 ( 𝑦=𝑥 )∆𝑋𝑌𝑍

x-axis x,y x, y

x,y x,y y-axis x,y y,xy = x

y = -x x,y y, x

Rules of REFLECTION

Reflect the object below over the x-axis and then the y-axis:Name the coordinates of the

original object: R

PD

R: (-9, 9)

P: (-8, 5)

D: (-2, 4)

U: (-9, 2)

D’

R’

P’

UName the coordinates of the

reflected object:R’’: (9, -9)

P’’: (8, -5)

D’’: (2, -4)

U’’: (9, -2)

How were the coordinates affected when the object was reflected over both the x-axis and y-axis?

U’

D’’P’’

U’’

R’’

Would it make a difference if we

reflected over the y-axis first and then the x-axis? Try it! Then

reflect about what you discovered.

How were the coordinates affected when the object

was reflected over both the x-axis and y-axis?

Would it make a difference if we

reflected over the y-axis first and then the x-axis? Try it! Then reflect about

what you discovered.

Would the result of this double reflection be the same as a rotation of the original

figure of 180°?

Think About It