Understanding 180° Rotation of a Triangle

The video tutorial explains how to rotate triangle ABC counterclockwise by 180° about the origin to form triangle A'B'C'. It begins by introducing the concept of rotation and then graphing triangle ABC with arbitrary points. The tutorial demonstrates the rotation of each point by 180° and identifies the pattern that emerges in the coordinates of the rotated points. The rule for this transformation is that each point (x, y) becomes (-x, -y) after rotation.

What transformation did Julia apply to triangle ABC?

• A 180° counterclockwise rotation

• A reflection over the x-axis

• A 90° clockwise rotation

• A translation along the y-axis

Why did the narrator choose arbitrary points for triangle ABC?

• To make the problem easier

• To visualize the rotation process

• To avoid using real data

• To confuse the viewer

What is the new position of point A after a 180° rotation about the origin?

• (-2, -3)

• (-3, -2)

• (3, 2)

• (2, 3)

How does the position of point B change after a 180° rotation?

• It moves to (-4, -1)

• It moves to (1, 4)

• It moves to (-1, -4)

• It moves to (4, 1)

What is the new position of point C after the rotation?

• (-6, -5)

• (-5, -6)

• (6, 5)

• (5, 6)

What pattern is observed in the coordinates after the rotation?

• The coordinates are halved

• The coordinates remain the same

• The coordinates are negated

• The coordinates are doubled

What happens to the distance from the origin after a 180° rotation?

• It becomes zero

• It remains the same

• It halves

• It doubles

What is the rule for the transformation of any point (x, y) after a 180° rotation?

• The point becomes (x, y)

• The point becomes (-x, -y)

• The point becomes (y, x)

• The point becomes (-y, -x)

Which of the following is true about the rotation of triangle ABC?

• The triangle is translated along the x-axis

• The triangle is reflected over the y-axis

• The triangle is rotated 90° clockwise

• The triangle is rotated 180° counterclockwise

What is the significance of the origin in this rotation?

• It is the point of reflection

• It is the center of rotation

• It is the midpoint of the triangle

• It is the endpoint of translation