Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but maintains its shape. It is defined by a center of dilation and a scale factor.

Front

What is the center of dilation?

Back

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

Front

How does a scale factor affect a dilation?

Back

The scale factor determines how much the figure is enlarged or reduced. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

If the center of dilation is at (0,0) and the scale factor is 2, what are the new coordinates of point (x,y)?

Back

The new coordinates will be (2x, 2y).

Front

What happens to the coordinates of a point (x,y) when dilated by a scale factor of 1/2?

Back

The new coordinates will be (1/2 * x, 1/2 * y).

Front

What is the algebraic rule for a dilation with a scale factor of 3?

Back

The algebraic rule is f(x,y) → (3x, 3y).

Front

How do you find the coordinates of a dilated triangle with vertices A(2,0), B(3,-1), C(-2,-5) and a scale factor of 3?

Back

Multiply each vertex's coordinates by the scale factor: A'(6,0), B'(9,-3), C'(-6,-15).

Front

What is the effect of a negative scale factor in dilation?

Back

A negative scale factor not only changes the size of the figure but also reflects it across the center of dilation.

Front

If point A is at (4,5) and is dilated with a center at (0,0) and a scale factor of -2, what are the new coordinates?

Back

The new coordinates will be (-8,-10).

Front

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

Back

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