Reflections and Dilations

Reflections and Dilations

Dilations

• Dilations make your image larger or smaller.

• Given a scale factor of k:

• (x, y) → (k⋅x, k⋅y)

Dilations continued:

• When finding a dilation, given a scale factor. All you must do is multiply the points of the given figure by the scale factor.

Multiple Choice

A triangle has vertices with coordinates (2,0), (3, -1) and (-2,-5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image?

• (5,3), (6,2), (1,-2)

• (6,0), (9,-3), (-6,-15)

• (2/3,0), (1,-1/3), (-2/3,-5/3)

• (-1,-3), (0,-4), (-5,-8)

Multiple Choice

State the coordinate of the image of the given point B (-10,-6) under a dilation with center at the origin with the given scale factor k = 1/2.

• (5,3)

• (20,12)

• (-20,-12)

• (-5,-3)

Multiple Choice

If the picture has a scale factor of 2, what will the point E' be?

(Click the picture to make it bigger.)

• (10, 6)

• (14, -2)

• (5, 3)

• (2, -2)

Finding a scale factor

• If you need to find the scale factor of a dilation, simply divide the post-image by the pre-image.

• A'/A

Multiple Choice

The point (8, 12) was dilated to become point (2, 3). What was the scale factor?

• ½

• ¼

• 4

• 2

Multiple Choice

Choose the correct scale factor:

• 2

• 3

• 1/3

• 1/2

Multiple Choice

Which is a dilation of 2?

Reflections

• A reflection is a flip over a given line or point.

• The mapping for a reflection is different given depending on where the line of reflection is located.

A reflection over an axis:

• A reflection over the x-axis is sometimes called a reflection over the line y = 0.

• A reflection over the x-axis can be mapped by:

• (x, y) → (x, -y)

• A reflection over the y-axis is sometimes called a reflection over the line x = 0.

• A reflection over the y-axis can be mapped by:

• (x, y) → (-x, y)

Multiple Choice

∆QRS contains the points: Q(4, 2) R(5, 1) S(3,7). If the triangle is reflected across the y-axis, what will S' be?

• S'(3, 7)

• S'(-3, 7)

• S'(-3, -7)

• S'(3, 7)

Multiple Choice

Find K' if the figure is reflected across the x-axis

• (4, 1))

• (-1, -4)

• (1, -4)

• (1, 4)

Multiple Choice

Which one is a reflection over the y-axis?

Multiple Choice

Which answer shows a reflection across the x-axis?

• d

• c

• b

• a

Multiple Choice

Identify the transformation from ABC to A'B'C'.

• Reflection across the x-axis

• Reflection across the y-axis

• 90^o clockwise rotation

• 90^o counterclockwise rotation

Reflecting over non-axes

It's possible to reflect over any line. We often reflect over y = x

or y = -x. These are easy to spot because the flip will look more like a rotation.

Reflecting over non-axes continued.

• When reflecting over a horizontal line, they will be of the form: y = a. (a is a positive or negative number.)

• When reflecting over a horizontal line, the y value will change, but not the x.

• When reflecting over a vertical line, they will be of the form: x = a.

• When reflecting over a vertical line, the x value will change, but not the y.

Multiple Choice

If we reflect this figure over the line y = 5. Where will P' be?

• (1, 1)

• (1, 4)

• (5, 9)

• (-1, 5)

Multiple Choice

If we reflect this figure across the line x = 2, where will N' be located?

• (-1, 3)

• (5, 1)

• (2, 3)

• (5, 3)

Multiple Choice

What is the line of reflection?

• x = 4

• x = 3

• y = 3

• y = 4

Multiple Choice

What is the line of reflection?

• x = 1

• y = 1

• x = 3

• x = 2