Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but not its shape, using a center of dilation and a scale factor.

Front

What is the scale factor in a dilation?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation.

Front

If a figure is dilated by a scale factor of 2, what happens to its size?

Back

The figure's size is doubled.

Front

What is the center of dilation?

Back

The center of dilation is a fixed point in the plane about which all points of a figure are expanded or contracted.

Front

How do you find the scale factor when given original and dilated coordinates?

Back

The scale factor can be found by dividing the distance from the center of dilation to the dilated point by the distance from the center of dilation to the original point.

Front

What happens to the coordinates of a point (x, y) when it is dilated by a scale factor k from the center (a, b)?

Back

The new coordinates will be (a + k(x - a), b + k(y - b)).

Front

If the point (4, 6) is dilated to (8, 12), what is the scale factor?

Back

The scale factor is 2.

Front

What is the effect of a scale factor less than 1 on a figure?

Back

A scale factor less than 1 reduces the size of the figure.

Front

If a quadrilateral is dilated with a scale factor of 1/2, what happens to its area?

Back

The area of the quadrilateral is reduced to 1/4 of its original area.

Front

What is the relationship between the scale factor and the area of a figure?

Back

If the scale factor is k, the area of the figure is multiplied by k².