Dilation of Lines and Points

The video tutorial explains the concept of line dilation in geometry, focusing on how lines can be dilated with respect to a center, typically the origin. It covers the effects of different scale factors and centers on the dilation process, resulting in lines that either map onto themselves or become parallel to the original. The tutorial includes both visual and algebraic methods for understanding dilation, supported by activities and examples using GeoGebra. The lesson concludes with a recap of the key concepts and their applications.

What happens to a point on the line y = x when it is dilated with a scale factor of 2 centered at the origin?

• The point moves to a new line.

• The point remains unchanged.

• The point moves to a new position on the same line.

• The point disappears.

If a point (2, 2) on the line y = x is dilated by a scale factor of 2, what will be the new coordinates of the point?

• (4, 4)

• (2, 2)

• (1, 1)

• (0, 0)

What is the result of dilating a line that does not pass through the origin with a scale factor of 2?

• The line becomes parallel to the original.

• The line becomes perpendicular to the original.

• The line remains the same.

• The line disappears.

When dilating a line with a new center, what is the first step in the algebraic method?

• Divide the point by the scale factor.

• Add the center coordinates to the point.

• Multiply the point by the scale factor.

• Subtract the center coordinates from the point.

In the visual representation of dilation, what does the new point represent?

• A point on a different line.

• A point that does not exist.

• A point on the same line but further away.

• A point on the same line but closer.

What is the effect of a dilation with a scale factor less than 1?

• The line becomes longer.

• The line becomes shorter.

• The line becomes perpendicular.

• The line remains unchanged.

In the GeoGebra activity, what does a dilation map a line not passing through the center to?

• A different line.

• The same line.

• A parallel line.

• A perpendicular line.

What happens to a line when it is dilated with a scale factor of 1?

• The line becomes longer.

• The line becomes shorter.

• The line remains the same.

• The line disappears.

If a line is dilated with a scale factor of 0.5, what happens to the points on the line?

• They move further apart.

• They remain unchanged.

• They move closer together.

• They disappear.

What is the result of dilating a line with a scale factor of 6 centered at point A?

• The line moves six times further away from point A.

• The line becomes six times shorter.

• The line remains unchanged.

• The line becomes six times longer.