Geometric Transformations and Reflections

The video tutorial explains how to write general rules for describing rotations of geometric figures. It covers two specific cases: a 180-degree counterclockwise rotation and a 90-degree counterclockwise rotation, both about the origin. The tutorial uses triangles XYZ and RST to demonstrate how the coordinates of points change after rotation. For a 180-degree rotation, the rule is to take the negative of both x and y coordinates. For a 90-degree rotation, the rule is to switch the coordinates and change the sign of the new x-coordinate. The video emphasizes that these rules depend on the degree of rotation.

What is the primary focus of the video tutorial?

• Writing general rules for translations

• Writing general rules for rotations and reflections

• Solving algebraic equations

• Understanding geometric shapes

Which of the following describes a reflection across the x-axis?

• (x, y) becomes (y, x)

• (x, y) becomes (x, -y)

• (x, y) becomes (-x, -y)

• (x, y) becomes (-x, y)

Which of the following describes a reflection across the y-axis?

• (x, y) becomes (-x, -y)

• (x, y) becomes (-x, y)

• (x, y) becomes (y, x)

• (x, y) becomes (x, -y)

What is the center of rotation for the triangle XYZ?

• Point Z

• The origin

• Point Y

• Point X

After a 180-degree rotation, what happens to the coordinates of a point?

• They remain the same

• They switch places

• They double in value

• They become negative

What is the general rule for a 180-degree rotation?

• (x, y) becomes (x, -y)

• (x, y) becomes (-x, -y)

• (x, y) becomes (-y, x)

• (x, y) becomes (y, x)

What happens to the signs of the coordinates in a 180-degree rotation?

• Only the x-coordinate changes

• Only the y-coordinate changes

• They both change

• They remain unchanged

What is the initial position of point R in triangle RST?

• (1, -5)

• (5, 1)

• (8, -2)

• (6, -4)

What is the initial position of point T in triangle RST?

• (5, 1)

• (8, -2)

• (1, -5)

• (6, -4)

After a 90-degree rotation, what happens to the coordinates of a point?

• They remain the same

• They become negative

• They double in value

• They switch places and the new x-coordinate changes sign