reflections

reflections

by Austin Castillo

​When we reflect on an axis, we must first understand which axis we are reflecting on.

​The x axis moves from left to right and the y axis moves up and down.

Multiple Choice

Which axis on a graph goes up and down?

• x

• origin

• symmetry

• y

Multiple Choice

Which axis on a graph goes side to side?

• x

• symmetry

• y

​When we reflect on the x axis, a point will "jump" over the x axis.

Each point is labeled by a coordinate ( X, Y )

​

​Notice when we reflect on the x axis, the

​height changes on the graph. This means we

​changed the Y value. (up and down)

Multiple Choice

What value changed on this x reflection?

• the x value

  (side to side)

• the y value

  (up and down)

​If the y value changed on a reflection on the x axis, then we can say that the (x,y) changed to (x,-y)

​We make the y a negative because it is the value that changed to the opposite number by going over the x axis.

​What happens when we reflect on the y axis?

​When we reflect on the y axis, we are changing the horizontal location.

​

This means we are changing the x value of the

​dots location. so it goes from

​xy --> (-x,y)

Multiple Choice

which value changed on the reflection on the y axis?

• the y value

  (up and down)

• the x value

  (side to side)

Multiple Choice

Is the picture an x axis reflection or a y-axis reflection? Which axis does it jump over?

• x

• y

Multiple Choice

Which axis does this reflection go over?

• x

• y

​So, for the algebraic representation we must show the change happening for each reflection

​on an x axis reflection the y value changes. xy -> x,-y

​

​on a y axis reflection, the x value changes. xy -> -x,y

​Ok, so we see a pattern here

​a reflection on the y axis, changes the x value (x,y) --> (-x,y)

​

​a reflection on the x axis, changes the y value (x,y) --> (x,-y)

​

​These are the rules you need to remember.

​Lets repeat it a bunch of times!

Fill in the Blank

Fill in the Blank

Multiple Choice

What is the algebraic representation when you reflect on the x axis?

• x,y -> x,-y

• x,y -> -x,y

Multiple Choice

What value changes when you reflect on the y axis?

• the x value

• the y value

Fill in the Blank

​open your books to page 71.

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