Transformations in Geometry

The video tutorial covers the concepts of translation and rotation on a coordinate plane. It begins with translating points and shapes, explaining how to write and combine translations. The tutorial then shifts to rotations, detailing how to rotate points around the origin and the effects of positive and negative rotations. The video emphasizes understanding through examples and encourages sketching to visualize transformations.

What is the result of translating the point (-2, 1) two units to the right and three units up?

• (0, 1)

• (0, 4)

• (2, 4)

• (-2, 4)

If you start at (4, 2) and translate three units left and five units down, where do you end up?

• (7, -3)

• (7, 3)

• (1, 3)

• (1, -3)

How do you express a translation that moves a point 3 units right and 2 units up?

• (X+2, Y+3)

• (X-2, Y-3)

• (X-3, Y-2)

• (X+3, Y+2)

What are the resulting coordinates when you apply the translation (X+4, Y-1) to the point (3, 5)?

• (3, 6)

• (3, 4)

• (7, 6)

• (7, 4)

If a point is translated by (X-2, Y+3) and ends up at (-3, 8), what were the original coordinates?

• (-5, 11)

• (-1, 11)

• (-5, 5)

• (-1, 5)

What is the single translation equivalent to performing (X+1, Y-1) followed by (X-5, Y-6)?

• (X+6, Y+5)

• (X-6, Y-5)

• (X+4, Y+7)

• (X-4, Y-7)

When translating a shape, what happens to each point in the shape?

• The shape is rotated

• Only the vertices are translated

• Only the center is translated

• Each point undergoes the same translation

What are the resulting coordinates when rotating the point (3, 4) by 90 degrees around the origin?

• (-4, 3)

• (4, -3)

• (-3, -4)

• (3, -4)

How do you rotate a point by 180 degrees around the origin?

• Flip the sign of both coordinates

• Swap the coordinates

• Add 180 to each coordinate

• Subtract 180 from each coordinate

What is the result of rotating the point (5, 2) by negative 90 degrees around the origin?

• (-5, 2)

• (-2, 5)

• (2, -5)

• (5, -2)