8.10 Transformations

Front

What is a transformation in geometry?

Back

A transformation in geometry is an operation that moves or changes a shape in some way to produce a new shape. The main types of transformations are translations, rotations, reflections, and dilations.

Front

Define translation in the context of transformations.

Back

Translation is a type of transformation that slides a shape from one position to another without turning it. The shape remains congruent and the distance and direction of the slide are defined by a vector.

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a shape around a fixed point, known as the center of rotation, by a certain angle in a specific direction (clockwise or counterclockwise).

Front

Explain reflection in geometry.

Back

Reflection is a transformation that flips a shape over a line, known as the line of reflection, creating a mirror image of the original shape.

Front

What is dilation in geometry?

Back

Dilation is a transformation that changes the size of a shape but keeps its proportions the same. It is defined by a center point and a scale factor.

Front

What is the difference between congruent and similar figures?

Back

Congruent figures are identical in shape and size, while similar figures have the same shape but may differ in size. Similar figures have proportional corresponding sides.

Front

How do you perform a translation on a point (3, 4) by the vector (2, -1)?

Back

To translate the point (3, 4) by the vector (2, -1), you add the vector components to the point's coordinates: (3 + 2, 4 - 1) = (5, 3).

Front

What is the effect of a 90-degree clockwise rotation on the point (1, 2)?

Back

A 90-degree clockwise rotation of the point (1, 2) around the origin results in the new point (2, -1).

Front

Describe the line of reflection for the point (3, 5) reflected over the line y = x.

Back

When reflecting the point (3, 5) over the line y = x, the coordinates are swapped, resulting in the new point (5, 3).

Front

What is the scale factor in a dilation that enlarges a shape by a factor of 3?

Back

The scale factor in a dilation that enlarges a shape by a factor of 3 is 3. This means that each point of the shape is moved away from the center of dilation by three times its original distance.