Line Dilations

Front

What is a line dilation?

Back

A transformation that alters the size of a line segment while maintaining its shape and orientation, centered at a specific point.

Front

What is a scale factor in dilation?

Back

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

If a line segment is dilated by a scale factor of 2, what happens to its length?

Back

The length of the line segment doubles.

Front

What is the relationship between the original line segment and its image after dilation?

Back

The original line segment and its image are parallel.

Front

How do you find the coordinates of a point after dilation?

Back

Use the formula: (x', y') = (kx + (1-k)x_c, ky + (1-k)y_c), where (x_c, y_c) is the center of dilation, k is the scale factor, and (x, y) are the original coordinates.

Front

What is the effect of a dilation centered at the origin on the equation of a line?

Back

The coefficients of the line's equation are multiplied by the scale factor.

Front

If the length of a line segment after dilation is 18 and the scale factor is 4, what was the original length?

Back

The original length was 4.5.

Front

What are the coordinates of point B(4, 3) after a dilation centered at A(3, 4) with a scale factor of 2?

Back

B' = (5, 2).

Front

What is the new equation of the line 3y = -2x + 8 after dilation by a scale factor of 2?

Back

The new equation is 2x + 3y = 5.

Front

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

Back

Length after dilation = Original length × Scale factor.