7-3 Dilations of Lines

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 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 and y-intercept may change.

Front

What happens to the y-intercept of a line when it is dilated?

Back

The y-intercept of a line will change when the line is dilated, depending on the center of dilation and the scale factor.

Front

If a line has the equation y = mx + b, what is the image of the line after dilation centered at the origin with scale factor k?

Back

The image will have the equation y = mx + (b * k), where m is the slope and b is the original y-intercept.

Front

What is the equation of a line after a dilation with a scale factor of 2 centered at the origin for the line y = 2x + 3?

Back

The image will be y = 2x + 6.

Front

What is the effect of a dilation centered at a point other than the origin?

Back

The image of the line will change its position and may have a different y-intercept, but the slope will remain the same.

Front

How do you find the new y-intercept after a dilation centered at a point (h, k)?

Back

To find the new y-intercept, apply the dilation transformation to the original y-intercept using the center of dilation.

Front

What is the relationship between the slopes of a line and its image after dilation?

Back

The slopes of the original line and its image after dilation are equal.

Front

If a line y = mx + b is dilated by a scale factor of 1, what is the image?

Back

The image will be the same as the original line: y = mx + b.