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 the scale factor is greater than 1, what happens to the figure?

Back

The figure is enlarged.

Front

If the scale factor is between 0 and 1, what happens to the figure?

Back

The figure is reduced.

Front

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

Back

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

Front

How do you find 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

What is the effect of a dilation centered at the origin?

Back

A dilation centered at the origin multiplies the coordinates of each point by the scale factor.

Front

What transformation occurs when the function f(x) = x^2 is changed to g(x) = (x + 4)^2?

Back

This is a horizontal translation 4 units to the left.

Front

What does the equation f(x) = 1/2(x + 9)^2 - 1 indicate about the parabola?

Back

It indicates a vertical compression by 1/2, a left shift of 9 units, and a downward shift of 1 unit.

Front

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

Back

A negative scale factor reflects the figure across the center of dilation.