Final answer:
Translations, rotations, reflections, and dilations are different types of transformations in mathematics. Translations move each point of a figure the same distance and in the same direction. Rotations turn a figure around a fixed point. Reflections flip a figure over a line. Dilations enlarge or reduce a figure by a scale factor.
Step-by-step explanation:
In mathematics, there are several transformations that can be applied to geometric figures. These transformations include translations, rotations, reflections, and dilations.
Translations:
A translation is a transformation in which each point of a figure is moved the same distance and in the same direction. For example, if we have a triangle and we move it 2 units to the right and 3 units up, we would describe it as a translation by (2, 3).
Rotations:
A rotation is a transformation in which a figure is turned around a fixed point called the center of rotation. The amount of rotation is determined by the angle of rotation. For example, if we rotate a square 90 degrees clockwise around its center, we would describe it as a rotation of 90 degrees.
Reflections:
A reflection is a transformation in which a figure is flipped over a line called the line of reflection. The line of reflection acts as a mirror. For example, if we reflect a triangle over the y-axis, we would describe it as a reflection over the y-axis.
Dilations:
A dilation is a transformation in which a figure is enlarged or reduced by a certain scale factor. The scale factor determines the amount of enlargement or reduction. For example, if we dilate a circle with a scale factor of 2, the resulting circle would have twice the radius of the original circle.