Dilations at the Origin

Line segment AB (pictured) is dilated with center (0,0) and scale factor k = 2. Segment A'B' will be...

• Parallel to segment AB and longer than segment AB

• In the same position as segment AB, but longer than segment AB

• Parallel to segment AB, and shorter than segment AB

• In the same position as segment AB, but shorter than segment AB

Line segment AB, pictured, is dilated with center (0,0) and scale factor k = 1/3 . Segment A'B' will be...

• Parallel to segment AB and longer than segment AB

• In the same position as segment AB, but longer than segment AB

• Parallel to segment AB, and shorter than segment AB

• In the same position as segment AB, but shorter than segment AB

Every dilation has 2 components, they are;

• Center of Dilation

  Scale Factor of Dilation

• Center of Dilation

  Origin of Dilation

• Scale Factor of Dilation

  Direction of Dilation

• Scale Factor of Dilation

  Distance of Dilation

Dilations produce...

• Congruent Figures

• Similar Figures

• Figures that have no relationship with each other

• Scale Factor of Dilation

  Distance of Dilation

The rule for an enlargement dilation is...

• (x,y) ---> (kx, ky), where k >1

• (x,y) ---> (kx, ky), where 0 < k < 1

• (x,y) ---> (x, ky), where k >1

• (x,y) ---> (kx, y), where k >1

Check all properties NOT preserved in a dilation

• Distance

• Angle measure

• Orientation

• Parallelism

• Collinearity

If the point (4, -6) is dilated with a scale factor of 2 centered at the origin, what are the coordinates of the image?

• (2, -3)

• (8, -12)

• (-8, 12)

• (4, -6)

What is the effect of a dilation with a scale factor of 1 centered at the origin?

• The figure is enlarged.

• The figure is reduced.

• The figure remains unchanged.

• The figure is reflected.

A triangle has vertices at (2, 3), (4, 5), and (6, 7). If the triangle is dilated with a scale factor of 0.5 centered at the origin, what are the coordinates of the new vertices?

• (1, 1.5), (2, 2.5), (3, 3.5)

• (1, 1.5), (2, 2.5), (4, 3.5)

• (4, 6), (8, 10), (12, 14)

• (1, 1.5), (2, 2.5), (3, 3.5)

What happens to the orientation of a figure after a dilation centered at the origin?

• It flips over the x-axis.

• It flips over the y-axis.

• It remains the same.

• It rotates 180 degrees.