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 point 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. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

How do you calculate the scale factor when given original and dilated points?

Back

The scale factor can be calculated by dividing the coordinates of the dilated point by the corresponding coordinates of the original point.

Front

If a point (x, y) is dilated by a scale factor k, what are the coordinates of the dilated point?

Back

The coordinates of the dilated point are (kx, ky).

Front

What is the effect of a scale factor of 1 on a figure during dilation?

Back

A scale factor of 1 means that the figure remains unchanged in size during the dilation.

Front

What happens to the coordinates of a point when it is dilated with a scale factor of 1/2?

Back

The coordinates of the point are multiplied by 1/2, resulting in a reduction of the distance from the origin.

Front

How do you find the image of a triangle after dilation?

Back

To find the image of a triangle after dilation, apply the dilation rule to each vertex of the triangle.

Front

What is the center of dilation?

Back

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

Front

If triangle ABC is dilated with a scale factor of 2, what happens to the lengths of its sides?

Back

The lengths of the sides of triangle ABC will be doubled.

Front

What is the relationship between the original figure and its dilated image?

Back

The original figure and its dilated image are similar, meaning they have the same shape but different sizes.