Exploring Translations in Geometry

This video tutorial introduces the concept of translations in mathematics, focusing on how two-dimensional figures move on a coordinate plane. It covers key vocabulary such as transformation, image, and congruence, and explains how to identify translations. The tutorial provides examples and practice exercises, demonstrating how to translate figures both visually and algebraically. It emphasizes the importance of congruence in translations and guides viewers through translating figures in the coordinate plane using ordered pairs.

What does a transformation in mathematics describe?

• A change in color of a figure

• A change in the size of the coordinate plane

• A change in the three-dimensional space

• A change in location or shape of a two-dimensional figure

Which of the following is NOT a type of transformation?

• Coloring

• Sliding

• Turning

• Flipping

What is a translation in mathematical terms?

• Changing the size of a figure

• Moving a figure left, right, up, or down without changing its orientation

• Reflecting a figure over a line

• Rotating a figure around a point

How is the image of a transformed figure indicated?

• By using a double apostrophe

• By using a prime symbol

• By underlining the figure's name

• By changing the figure's color

What must be true for a transformation to be considered a translation?

• The figure must change color

• The figure must rotate

• The figure must increase in size

• The figure must remain congruent to its original

How do you perform a translation of a figure in the coordinate plane?

• By increasing the size of the figure

• By changing the figure's color

• By adding or subtracting from the x and y coordinates

• By rotating each point around the origin

What does translating a figure 8 units to the right and 3 units down involve?

• Subtracting 8 from the x-coordinate and adding 3 to the y-coordinate

• Adding 8 to the y-coordinate and subtracting 3 from the x-coordinate

• Adding 8 to the x-coordinate and subtracting 3 from the y-coordinate

• Rotating the figure 8 degrees clockwise and then 3 degrees counterclockwise

What indicates that a figure has been translated correctly on a coordinate plane?

• The figure changes orientation

• The figure's size increases

• The figure remains congruent to its original

• The figure's color changes

When translating a figure, what does moving it 6 units to the left and 4 units up mean?

• Reflect the figure over the x-axis and then over the y-axis

• Rotate the figure 6 degrees to the left and then 4 degrees up

• Add 6 to the x-coordinate and subtract 4 from the y-coordinate

• Subtract 6 from the x-coordinate and add 4 to the y-coordinate

What is the result of translating a figure according to the rule: x becomes x-6, y becomes y+4?

• The figure increases in size

• The figure rotates 6 units clockwise

• The figure moves 6 units left and 4 units up

• The figure moves 6 units right and 4 units down