In Saxon Math Course 2, Grade 7 students learn about the three types of geometric transformations — reflection, translation, and rotation — and how to perform each on figures plotted on a coordinate plane. The lesson covers how flipping a shape across the x- or y-axis produces a reflection, sliding it to a new position creates a translation, and turning it around a center of rotation results in a rotation. Students practice identifying and drawing transformed figures using ordered pairs and prime notation for image vertices.
Section 1
📘 Transformations
Transformations move or resize geometric figures. The main types are reflections (flips), translations (slides), rotations (turns), and dilations (resizing).
| Movement | Name |
|---|---|
| flip | reflection |
| slide | translation |
| turn | rotation |
This is your introduction to the four types of transformations. Next, you'll work through examples showing how to graph each one on a coordinate plane.
Section 2
Transformations
These 'flips, slides, and turns' are called transformations.
| Movement | Name |
| :--- | :--- |
| flip | reflection |
| slide | translation |
| turn | rotation |
A flip over the y-axis is a reflection: A point at moves to .
A slide 4 units down is a translation: A point at moves to .
A spin around the origin is a rotation: A point at moves to .
Transformations are the super moves for shapes! You can flip them like a pancake (reflection), slide them like a video game character (translation), or spin them like a top (rotation). These moves change a figure's position or orientation on the page, but the shape itself stays the exact same size, making it congruent.
Section 3
Reflection
A reflection of a figure in a line (a 'flip') produces a mirror image of the figure that is reflected.
Reflecting with vertices in the x-axis gives .
Reflecting the point in the y-axis results in the point .
When you reflect a point across the x-axis, the new point becomes .
Imagine a puddle on the ground. A reflection is your shape's twin looking back at it from the other side of a line, like the edge of the puddle. Every point is the same distance from the line, just on the opposite side. This creates a perfect, spooky mirror image of the original figure!
Section 4
Translation
A translation 'slides' a figure to a new position without turning or flipping the figure.
Translating rectangle with vertex left 6 units and down 3 units moves to .
If point is translated right 2 units and up 1 unit, its new position is .
To translate a point by , the new coordinates are .
A translation is like pushing a chess piece across the board. The shape doesn't twist, turn, or flip; it just glides to a new location. Every single point on the shape moves the exact same distance and in the exact same direction. It's a perfectly synchronized group trip for all the points!
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Section 1
📘 Transformations
Transformations move or resize geometric figures. The main types are reflections (flips), translations (slides), rotations (turns), and dilations (resizing).
| Movement | Name |
|---|---|
| flip | reflection |
| slide | translation |
| turn | rotation |
This is your introduction to the four types of transformations. Next, you'll work through examples showing how to graph each one on a coordinate plane.
Section 2
Transformations
These 'flips, slides, and turns' are called transformations.
| Movement | Name |
| :--- | :--- |
| flip | reflection |
| slide | translation |
| turn | rotation |
A flip over the y-axis is a reflection: A point at moves to .
A slide 4 units down is a translation: A point at moves to .
A spin around the origin is a rotation: A point at moves to .
Transformations are the super moves for shapes! You can flip them like a pancake (reflection), slide them like a video game character (translation), or spin them like a top (rotation). These moves change a figure's position or orientation on the page, but the shape itself stays the exact same size, making it congruent.
Section 3
Reflection
A reflection of a figure in a line (a 'flip') produces a mirror image of the figure that is reflected.
Reflecting with vertices in the x-axis gives .
Reflecting the point in the y-axis results in the point .
When you reflect a point across the x-axis, the new point becomes .
Imagine a puddle on the ground. A reflection is your shape's twin looking back at it from the other side of a line, like the edge of the puddle. Every point is the same distance from the line, just on the opposite side. This creates a perfect, spooky mirror image of the original figure!
Section 4
Translation
A translation 'slides' a figure to a new position without turning or flipping the figure.
Translating rectangle with vertex left 6 units and down 3 units moves to .
If point is translated right 2 units and up 1 unit, its new position is .
To translate a point by , the new coordinates are .
A translation is like pushing a chess piece across the board. The shape doesn't twist, turn, or flip; it just glides to a new location. Every single point on the shape moves the exact same distance and in the exact same direction. It's a perfectly synchronized group trip for all the points!
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter