Debug
reflection animation

Reflect a Point

Across x axis, y axis and other lines

A reflection is a kind of transformation. It is basically a 'flip' of a shape over the line of reflection.

Reflections can be described using coordinates which allow us to easily describe the image and its preimage .

Formula List

  • Reflect over x-axis $$ (a,b) \rightarrow (a, \red - b)$$
    • Ex. $$(3,4) \rightarrow (3 ,\red - 4) $$ more
  • y-axis $$ (a,b) \rightarrow (\red - a, b)$$
    • Ex. $$(3,4) \rightarrow (\red - 3 ,4) $$ more
  • line $$y = x $$ $$ (a,b) \rightarrow (b, a)$$
    • Ex. $$(3,4) \rightarrow (4, 3) $$ more
  • line $$y = -x $$ $$ (a,b) \rightarrow (\red - b, \red - a )$$
    • Ex. $$(3,4) \rightarrow (\red - 4 ,\red - 3) $$ more

Most Common Types of Reflections

Reflection over the x-axis

A reflection over the x-axis can be seen in the picture below in which point A is reflected to its image A'. The general rule for a reflection over the x-axis:

$ (A,B) \rightarrow (A, -B) $

Reflection in the y-axis

A reflection in the y-axis can be seen in the picture below in which A is reflected to its image A'.

The general rule for a reflection in the y-axis:

$ (A,B) \rightarrow (-A, B) $

Reflection over the line $$ y = x $$

A reflection in the line y = x can be seen in the picture below in which A is reflected to its image A'.

The general rule for a reflection in the $$ y = x $$ :

$ (A,B) \rightarrow (B, A ) $

Reflection over the line $$ y = -x $$

A reflection in the line y = x can be seen in the picture below in which A is reflected to its image A'.

The general rule for a reflection in the $$ y = -x $$ :

$ (A,B) \rightarrow (\red - B, \red - A ) $

Reflections Applet

y =
m
x +
c

Select Reflection Line

Select Shape To reflect

Select If You Want Auto Flip For Shapes

Or Use This Button To Flip

Practice Problems

Perform the reflections indicated below

Problem 1

What is the image of point A(1,2) after reflecting it across the x-axis. In technical speak, pefrom the following transformation r(x-axis)?

Picture of reflection across y axis
Problem 2

What is the image of point A (31,1) after reflecting it across the x-axis. In technical speak, pefrom the following transformation r(y-axis)?

Picture of reflection across y axis
Problem 3

What is the image of point A(-2,,1) after reflecting it across the the line y = x. In technical speak, pefrom the following transformation r(y=x)?

Picture of reflection across y axis

Problems II

Problem 4

Point Z is located at $$ (2,3) $$ , what are the coordinates of its image $$ Z'$$ after a reflection over the x-axis

Remember to reflect over the x-axis , just flip the sign of the y coordinate.
$ (2,3) \rightarrow (2 , \red{-3}) $
Problem 5

Point Z is located at $$ (-2, 5) $$ , what are the coordinates of its image $$ Z'$$ after a reflection over the line $$y=x$$

Remember to reflect over the line y =x , you just swap the x and y coordinate values.
$ ( -2 , 5 ) \rightarrow ( 5 , -2 ) $
Problem 6

Point Z is located at $$ (-11,7) $$ , what are the coordinates of its image $$ Z'$$ after a reflection over the y-axis

Remember to reflect over the y-axis , you just flip the sign of the x coordinate.
$ ( -8 ,7 ) \rightarrow ( \red 8 , 7 ) $
Problem 7

Point Z is located at $$ (-3, -4 ) $$ , what are the coordinates of its image $$ Z'$$ after a reflection over the x-axis

Remember to reflect over the x-axis , just flip the sign of the y coordinate.
$ (-3, -4 ) \rightarrow (-3 , \red{4}) $

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