Transformations - Rigid Motions

What is the result of translating the point (2, 3) by the vector (4, -1)?

• (6, 2)

• (5, 3)

• (4, 4)

• (2, 2)

What is the transformation that moves a point from (1, 1) to (4, 5)?

• A translation described by the vector (3, 4)

• A rotation of 90 degrees clockwise

• A reflection over the line y = x

• A dilation with a scale factor of 3

What is the formula for a translation that moves a point left by 3 and up by 2?

• T(x, y) = (x + 3, y - 2)

• T(x, y) = (x - 3, y + 2)

• T(x, y) = (x - 2, y + 3)

• T(x, y) = (x + 2, y - 3)

What does it mean for a transformation to be rigid?

• A rigid transformation preserves the shape and size of a figure, meaning the distances between points remain unchanged.

• A rigid transformation alters the shape but not the size of a figure.

• A rigid transformation changes both the shape and size of a figure.

• A rigid transformation only affects the position of a figure without changing its dimensions.

What is a translation in geometry?

• A type of transformation that rotates a figure around a point.

• A type of transformation that moves every point of a figure the same distance in a specified direction.

• A type of transformation that reflects a figure across a line.

• A type of transformation that changes the size of a figure.

How do you describe a reflection across the line y = x?

• Reflecting a point (x, y) across the line y = x results in the new coordinates (y, x).

• Reflecting a point (x, y) across the line y = x results in the new coordinates (x, -y).

• Reflecting a point (x, y) across the line y = x results in the new coordinates (-x, y).

• Reflecting a point (x, y) across the line y = x results in the new coordinates (-y, -x).

What is the difference between a translation and a rotation?

• A translation turns a figure around a point, while a rotation slides a figure without changing its orientation.

• A translation slides a figure without changing its orientation, while a rotation turns a figure around a point.

• A translation and a rotation are the same thing.

• A translation changes the size of a figure, while a rotation changes its color.

What is the effect of a 90-degree clockwise rotation on a point (x, y)?

• (y, -x)

• (-y, x)

• (x, -y)

• (-x, -y)

What does it mean to reflect a point across the y-axis?

• To create a mirror image of the point on the opposite side of the y-axis, changing the sign of the x-coordinate.

• To move the point vertically up or down along the y-axis without changing its x-coordinate.

• To rotate the point 180 degrees around the origin.

• To translate the point horizontally along the x-axis without changing its y-coordinate.

What is the effect of a 180-degree rotation on a point (x, y)?

• The new coordinates are (x, y)

• The new coordinates are (y, x)

• The new coordinates are (-x, -y)

• The new coordinates are (x, -y)