Translations
True or False: Translations preserve the shape and size of a figure
True
What happens to the orientation of a figure during a reflection?
During a reflection, the orientation of a figure is flipped or mirrored across a line called the line of reflection.
What is a rotation in geometry?
A rotation in geometry is a transformation that turns a figure around a fixed point called the center of rotation.
What is a two-dimensional coordinate plane?
A two-dimensional coordinate plane is a flat surface divided into four quadrants by two perpendicular number lines
How do you plot a point on a coordinate plane?
To plot a point on a coordinate plane, you locate the x-coordinate on the x-axis and the y-coordinate on the y-axis, then mark the point where the two axes intersect.
Explain how to perform a translation using coordinate rules
Add the horizontal shift to the x-coordinate and the vertical shift to the y-coordinate
How are reflections used in architecture and design?
Reflections are used in architecture and design to create symmetrical patterns and designs, such as in the layout of tiles or the placement of mirrors.
A shape is rotated 180 degrees clockwise about the origin. If the original shape was symmetrical, will the rotated shape still be symmetrical? Justify your answer.
If the original shape were symmetrical, the rotated shape would also be symmetrical. Rotations preserve the symmetry of a figure.
What are the two axes of a coordinate plane?
X-axis and Y-axis
True or False: The x-coordinate is always listed first when giving the coordinates of a point.
True
Triangle ABC is translated 7 units to the right. If point A's original coordinates were (3, 5), what are its coordinates in the translated triangle?
10,5
Define the term "line of reflection."
The line of reflection is the line that acts as the mirror for the reflection. It divides the figure into two congruent halves.
Define the term "angle of rotation."
the angle of rotation is the measure of how much a figure is turned during a rotation.
Plot the point with coordinates (3, -2) on a coordinate plane.
Seen on paper
Explain how the coordinates of a point determine its location on a coordinate plane.
The coordinates of a point determine its location on a coordinate plane by specifying its horizontal and vertical position relative to the origin.
Provide an example of a real-life scenario where a translation might be used.
Moving furniture
A shape is reflected over the y-axis. If the original shape was symmetrical, will the reflected shape still be symmetrical? Justify your answer.
If the original shape was symmetrical, the reflected shape would also be symmetrical. Reflections preserve the symmetry of a figure.
Provide an example of a real-life scenario where a rotation might be used.
rotating a satellite dish
rotating to change directions in a vehicle
clock hand rotating around a clock
In which quadrant is a point located if its coordinates are (-4, 5)?
Q1
Plot the point with coordinates (4, 6) on a coordinate plane.
Seen on paper
A shape is translated 9 units to the right and 2 units down. If the original shape was equilateral, will the translated shape still be equilateral? Justify your answer.
Yes, An equilateral shape is a type of polygon where all sides are of equal length. When you translate a shape, each point is moved by the same amount in the same direction, so the relative distances between the points remain unchanged
Explain how to predict the result of a reflection on a shape without performing the actual reflection.
To predict the result of a reflection on a shape without performing the actual reflection, you can imagine the shape being flipped or mirrored across the line of reflection.
Explain how to predict the result of a rotation on a shape without performing the actual rotation.
To predict the result of a rotation on a shape without performing the actual rotation, you can imagine the shape being turned around the center of rotation by the given angle and direction.
How are coordinate planes used in mapping and navigation?
Coordinate planes are used in mapping and navigation to represent geographic locations and determine distances between points.
How are plotting points used in creating geometric shapes and patterns?
Plotting points are used in creating geometric shapes and patterns to create symmetrical designs, tessellations, and fractals.