Transformations - Isometries

Front

What is a transformation in geometry?

Back

A transformation is a function that maps a geometric figure onto another figure, changing its position, size, or orientation.

Front

What are isometries?

Back

Isometries are transformations that preserve distances and angles, meaning the original figure and the transformed figure are congruent.

Front

What is the rule for a translation?

Back

A translation moves every point of a figure the same distance in a specified direction.

Front

What is the translation rule for moving a point (x,y) to (x+9, y+4)?

Back

The translation moves the point 9 units to the right and 4 units up.

Front

What is a reflection in geometry?

Back

A reflection is a transformation that flips a figure over a line, creating a mirror image.

Front

What is the line of reflection for a reflection across y = x?

Back

The line of reflection is the line where every point on the original figure is equidistant from the line y = x.

Front

What does it mean for two geometric figures to be congruent?

Back

Two geometric figures are congruent if they have the same size and shape.

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, called the center of rotation, by a certain angle.

Front

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

Back

The new coordinates after a 90-degree clockwise rotation are (y, -x).

Front

What is the effect of a reflection over the x-axis on a point (x,y)?

Back

The new coordinates after a reflection over the x-axis are (x, -y).