Line 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 scale factor and a center of dilation.

Front

What does the scale factor in a dilation represent?

Back

The scale factor indicates how much larger or smaller the image will be compared to the original figure. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

How does dilation affect the slope of a line?

Back

The slope of a line remains unchanged during a dilation; only the position of the line may change.

Front

What happens to the y-intercept of a line during a dilation?

Back

The y-intercept of a line may change during a dilation, depending on the scale factor and the center of dilation.

Front

If a line segment is dilated by a scale factor of 2, what can be said about the lengths of the original and the image line segments?

Back

The image line segment will be twice the length of the original line segment.

Front

What is the relationship between two line segments that are dilated from the same center?

Back

The two line segments will be parallel to each other.

Front

How do you find the length of a line segment after dilation?

Back

To find the length of a line segment after dilation, multiply the original length by the scale factor.

Front

What is the formula for the equation of a line in slope-intercept form?

Back

The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the effect of a dilation centered at the origin on the coordinates of a point (x, y)?

Back

The coordinates of the point (x, y) after dilation by a scale factor k will be (kx, ky).

Front

If a line segment AB is dilated to A'B' with a scale factor of 1/2, how do the coordinates of A' and B' relate to A and B?

Back

The coordinates of A' and B' will be half of the coordinates of A and B, respectively.