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8th Grade TAKS Review 2008

Objective 3

Day 1

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Dilations• A Dilation is the enlargement or reduction of a

figure

• Every Dilation must have a Scale Factor

• A Scale Factor < 1 (less than 1) indicates a reduction

• A Scale Factor > 1 (greater than 1) indicates an enlargement

• On the coordinate grid, simply multiply each point by the scale factor

Obj. 3: 8.6A

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Dilations, cont…• Example: ΔTUV has vertices T(-2,3), U(2,2), and

V(-2,-3). ΔTUV is dilated by a scale factor of 2 and has the origin as the center of dilation. What are the coordinates of U’?

A.(-4, 6)

B.(4, 4)

C.(-4, -6)

D.(-2, -3)

(2, 2) times 2 = (4, 4)

Obj. 3: 8.6A

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Dilations, cont…• Identifying the scale factor when you

don’t have a coordinate grid…

• Find a pair of corresponding sides that you know

• Place the sides into a ratio (fraction)

• KEEP THE ORDER OF THE SHAPES IN MIND!

Obj. 3: 8.6A

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Dilations, cont…• Example: ΔABC ~ ΔMNO is shown below.

Which scale factor was used to transform ΔMNO to ΔABC?

A

B

CM

NO

A. 5

B.

C. 3.33

D.

153

22

4.5

1

5

3

10

ΔABCΔMNO:

153

:

1 : 5

Because our triangle became larger (enlargement) we choose the answer >1

Obj. 3: 8.6A

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Transformations• Four types of Transformations

• Translation (slide)

• Reflection (flip over)

Obj. 3: 8.6AB

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Translations

• After you have identified the problems as a translation

• Determine the right/left shift and the up/down shift

• Repeat the process for each point

• The new shape should look identical to the old one, just in a different place

Obj. 3: 8.6B

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Translations, cont…• Example: ΔDEF is translated 3 units to the

right and 3 units down. Which coordinate pair best represents F’?

A.(4, 2)

B.(-1, -3)

C.(3, -6)

D.(0, -3)

F’

D’

Obj. 3: 8.6B

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Reflections

• After you have identified the problem as a

reflection

• Determine the line that the image will

reflect over (the x or y-axis)

• Reflect each point over the indicated line

Obj. 3: 8.6B

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Reflections, cont…• Example: ΔMNO is shown on the coordinate

plane below. What will be the coordinates of N’ if ΔMNO is reflected across the x-axis?

A.(-4, -3)

B.(-1, -5)

C.(3, -2)

D.(1, 5)

(3, -2)

(-1, -5)

(-4, -3)

Obj. 3: 8.6B

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Views of 3-D Solids• You must be able to imagine a 3-D solid

from every angle

Top

Front

Front

Right

Left

Right

Left

13 2

2

1

1

Obj. 3: 8.7A

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Views of 3-D Solids, cont…• Example: Match the three views of this

solid to its 3-dimensional sketch.

Front Right Top

A. B. C. D.

Obj. 3: 8.7A

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Vocabulary• Transformation – a change made to a shape• Dilation – to make a shape bigger or smaller• Scale Factor – the number of times larger a shape

becomes• Enlargement – to make a shape larger• Reduction – to make a shape smaller• Translation – to slide a shape• Reflection – to flip a shape over a line• 3-dimensional – figure with length, width, and height