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Transformations on the Coordinate Plane Solutions

• The Coordinate Plane is made up by a horizontal number line, the    x-axis   , and a vertical number line, the    y-axis   . 

• Each coordinate $\underline{ \mathbf{(}\mathit{x}\mathbf{,}\mathbf{ }\mathit{y}\mathbf{)} }$ represents a point on the coordinate plane.
• A    reflection    is a mirror image after a shape or graph has been flipped over the line of reflection.
• A translation is a    shift   , either horizontal, vertical, or both, on the coordinate plane.


To reflect a figure over the x-axis:

• Label each vertex as $\left(x, y\right)$.
• Each point $\left(x, y\right)$ will become $\underline{ \mathbf{(}\mathit{x}\mathbf{,}\mathbf{ }\mathbf{–}\mathit{y}\mathbf{)} }$ in the reflected image.

To reflect a figure over the y-axis

• Label each vertex as $\left(x, y\right)$.
• Each point $\left(x, y\right)$ will become $\underline{\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{–}\mathit{x}\mathbf{,}\mathbf{ }\mathit{y}\mathbf{)}\mathbf{ }\mathbf{ }\mathbf{ }}$ in the reflected image.

To translate a point horizontally:
 

•    Subtract    the horizontal translation from the    x   -coordinate to move the point to the left.
 
•    Add    the horizontal translation to the    x   -coordinate to move the point to the right. 


To translate a point vertically:

• 
Subtract the vertical translation from the    y   -coordinate to move the point    down   .
• 
Add the vertical translation to the    y   -coordinate to move the point    up   . 

• To translate a figure, translate each    vertex    based on the given translation.

Example 1

Reflect or translate the coordinate $\mathbf{(}\mathbf{–}\mathbf{3}\mathbf{,}\mathbf{ }\mathbf{5}\mathbf{)}$ on the graph. 

Example 2

Reflect the figure over the given axis.

Example 3

Translate the figure.