Transformations and Dilations in Geometry

The video tutorial reviews algebraic representations of transformations, including translation, reflection, rotation, and dilation. It explains the rules for each transformation type and provides examples to illustrate their application. The tutorial emphasizes the importance of understanding these algebraic rules for efficient problem-solving, especially when the origin is the center of transformation.

What is the new coordinate of a point (X, Y) after a translation of 3 units right and 5 units up?

• (X-3, Y-5)

• (X+3, Y-5)

• (X+3, Y+5)

• (X-3, Y+5)

When reflecting a point across the X-axis, which coordinate changes its sign?

• X-coordinate

• Y-coordinate

• Both coordinates

• Neither coordinate

What happens to the coordinates of a point after a 180-degree rotation around the origin?

• They switch places

• They remain the same

• Only the X-coordinate changes sign

• They both change signs

If a point (X, Y) is rotated 90 degrees clockwise, what will be the new coordinates?

• (-Y, X)

• (Y, -X)

• (X, Y)

• (-X, -Y)

What is the result of applying a dilation with a scale factor of 2 to a point (X, Y)?

• (X/2, Y/2)

• (2X, 2Y)

• (X-2, Y-2)

• (X+2, Y+2)

In a dilation, what is the role of the scale factor?

• It switches the coordinates

• It changes the sign of the coordinates

• It is used to multiply the coordinates

• It determines the direction of the transformation

What is the algebraic rule for reflecting a point across the Y-axis?

• (Y, X)

• (-X, -Y)

• (-X, Y)

• (X, -Y)

How do you determine the new coordinates after a 270-degree rotation counterclockwise?

• Keep coordinates the same

• Change sign of both X and Y

• Switch X and Y, change sign of new Y

• Switch X and Y, change sign of new X

What is the effect of a 90-degree counterclockwise rotation on the coordinates of a point?

• Switch X and Y, change sign of new Y

• Change sign of both X and Y

• Keep coordinates the same

• Switch X and Y, change sign of new X

If a square with vertices at (-6, 0), (0, 6), (6, 0), and (0, -6) is dilated by a factor of 3, what are the new coordinates of the vertex originally at (6, 0)?

• (18, 6)

• (6, 18)

• (0, 18)

• (18, 0)