Geometric Transformations (Translation, Reflection, Rotation)

Front

What is a geometric transformation?

Back

A geometric transformation is a function that moves or changes a shape in a specific way, such as translation, reflection, or rotation.

Front

Define translation in geometry.

Back

Translation is a type of transformation that slides a shape from one position to another without changing its size, shape, or orientation.

Front

What are the coordinates of a point after a translation of T(3, 2) from point A(1, 1)?

Back

A'(4, 3) - The new coordinates are found by adding the translation values to the original coordinates.

Front

Define reflection in geometry.

Back

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

Front

What is the line of reflection for the point A(2, 3) reflected to A'(2, -3)?

Back

The line of reflection is the x-axis, as the y-coordinates change sign.

Front

Define rotation in geometry.

Back

Rotation is a transformation that turns a shape around a fixed point, known as the center of rotation, by a certain angle.

Front

What are the coordinates of point B(3, 4) after a 90-degree rotation counterclockwise around the origin?

Back

B'(-4, 3) - The coordinates change according to the rotation rules.

Front

What is the composition of transformations?

Back

A composition of transformations is when two or more transformations are combined to produce a single transformation.

Front

If a triangle is translated by T(2, -3) and then reflected over the y-axis, what is the final transformation?

Back

The final transformation can be expressed as a composition: R(y-axis) ∘ T(2, -3).

Front

What is the effect of a rotation of 180 degrees on point C(1, 2)?

Back

C'(-1, -2) - The point is rotated to the opposite quadrant.