Transformations

Front

What is a transformation in geometry?

Back

A transformation is a mathematical operation that moves or changes a shape in some way, including translations, rotations, reflections, and dilations.

Front

Define reflection in geometry.

Back

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

Front

What are the coordinates of a point after reflecting across the y-axis?

Back

If a point has coordinates (x, y), after reflecting across the y-axis, the new coordinates will be (-x, y).

Front

What happens to the coordinates of a point when it is reflected across the x-axis?

Back

If a point has coordinates (x, y), after reflecting across the x-axis, the new coordinates will be (x, -y).

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.

Front

How do you rotate a point 90° clockwise about the origin?

Back

To rotate a point (x, y) 90° clockwise about the origin, the new coordinates will be (y, -x).

Front

What is dilation in geometry?

Back

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

Front

If a shape is dilated by a scale factor of 2, what happens to its area?

Back

If a shape is dilated by a scale factor of k, the area of the shape is multiplied by k². So, if k=2, the area is multiplied by 4.

Front

What is the scale factor if the original length is 5 units and the new length is 12 units?

Back

Front

How do you find the area of a shape after dilation?

Back

To find the area after dilation, multiply the original area by the square of the scale factor.