Dilation of Lines and Their Properties

The video tutorial covers the concept of dilations, focusing on how to dilate lines in the coordinate plane. It provides step-by-step examples of dilating lines with different scale factors, highlighting the resulting changes in slope and y-intercept. The tutorial also identifies patterns and shortcuts in dilations, emphasizing that the slope remains unchanged while the y-intercept is multiplied by the scale factor. Additionally, it explains the special case when the center of dilation is on the line, resulting in the line remaining unchanged.

What is the first step in dilating a line?

• Draw the new line

• Calculate the y-intercept

• Find the slope of the line

• Pick two points from the original line

After dilating the point (1, 4) with a scale factor of 3, what is the new point?

• (0, 6)

• (1, 4)

• (2, 8)

• (3, 12)

What is the equation of the line after dilating y = 2x + 2 with a scale factor of 3?

• y = 6x + 6

• y = 6x + 2

• y = 2x + 6

• y = 2x + 2

What is the y-intercept of the line y = 2x + 2 after a dilation with a scale factor of 2?

• 2

• 0

• 4

• 6

What pattern is observed when dilating a line from the origin?

• The slope remains the same

• The y-intercept remains the same

• The line becomes perpendicular

• The slope changes

What is the y-intercept of the line y = 2x - 4 after a dilation with a scale factor of 3/2?

• -2

• -4

• -6

• 0

What is the equation of the line y = 2x - 4 after a dilation with a scale factor of 3/2?

• y = 3x - 6

• y = 3x - 4

• y = 2x - 6

• y = 2x - 4

What happens to the y-intercept when a line is dilated from the origin?

• It becomes zero

• It is multiplied by the scale factor

• It is divided by the scale factor

• It remains the same

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

• y = 3x + 2

• y = 6x + 2

• y = 6x

• y = 3x

What is the result of dilating a line when the center of dilation is on the line?

• The line remains the same

• The y-intercept changes

• The line becomes perpendicular

• The slope changes