Transformations and Reflections in Geometry

The video tutorial explains how to perform multiple geometric transformations on a triangle. It starts with rotating triangle ABC 180 degrees about the origin, followed by translating the rotated points along a vector. Finally, the points are reflected across the y-axis. Each transformation is marked with tick marks to indicate the number of transformations applied.

What is the first step in the sequence of transformations described?

• Scaling the triangle

• Translating the triangle

• Rotating the triangle

• Reflecting the triangle

What is the initial shape used for transformations?

• Rectangle PQRS

• Triangle ABC

• Circle O

• Square ABCD

How are the coordinates changed during a 180-degree rotation about the origin?

• The x-coordinates are doubled

• The signs of all coordinates are changed

• The y-coordinates are halved

• The coordinates remain the same

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

• (3, 1)

• (-3, -1)

• (1, 3)

• (-1, -3)

What vector is used to translate the rotated triangle?

• (1, -3)

• (-1, 3)

• (3, 1)

• (2, -2)

After translation, what is the new position of point B?

• (3, -5)

• (2, -2)

• (1, -1)

• (4, -2)

How many tick marks does a point have after two transformations?

• None

• Three

• Two

• One

What is the final transformation applied to the triangle?

• Rotation

• Scaling

• Reflection

• Translation

What happens to the x-coordinates during reflection across the y-axis?

• They are doubled

• Their signs are changed

• They remain the same

• They are halved

What is the final position of point C after all transformations?

• (-1, -1)

• (1, 1)

• (2, 2)

• (-2, -2)