Transformations in Geometry

The video tutorial covers transformational geometry, including translations, reflections, rotations, dilations, and compositions of transformations. It explains how to translate points, reflect shapes over the y-axis, rotate triangles around the origin, and apply dilations with scale factors. The tutorial also discusses combining multiple transformations to map figures onto each other.

What is the primary focus of transformational geometry?

• Transformations of shapes

• Algebraic expressions

• Statistics

• Calculus

Which transformation involves shifting a point left, right, up, or down?

• Reflection

• Dilation

• Translation

• Rotation

If a point moves from (-3, 4) to (4, 1), what is the translation rule?

• x + 5, y - 7

• x - 7, y + 5

• x - 5, y + 7

• x + 7, y - 5

What is the primary effect of a translation on a shape?

• It moves the shape without altering its size or orientation

• It changes the shape's orientation

• It reflects the shape

• It changes the shape's size

What happens to the x-coordinate when a point is reflected over the y-axis?

• It becomes negative

• It becomes positive

• It remains the same

• It doubles

If point C is at (5, 1) and is reflected over the y-axis, what are the new coordinates?

• (5, -1)

• (-5, 1)

• (1, 5)

• (-1, 5)

How does a reflection over the y-axis affect the coordinates of a point?

• Both coordinates are negated

• The y-coordinate is negated

• Neither coordinate is changed

• The x-coordinate is negated

What is the effect of a reflection over the y-axis on the coordinates of a point?

• Both coordinates are negated

• Neither coordinate is changed

• The y-coordinate is negated

• The x-coordinate is negated

What is the result of a 90° counterclockwise rotation of point (5, 4) around the origin?

• (-5, -4)

• (-4, 5)

• (4, -5)

• (5, 4)

Which formula is used for a 90° counterclockwise rotation?

• (x, y) -> (x, y)

• (x, y) -> (-x, -y)

• (x, y) -> (-y, x)

• (x, y) -> (y, -x)