1. 8th Grade TAKS Review 2008
Objective 3
Day 1

2. 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

3. 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’?
(2, 2) times 2 = (4, 4)
(-4, 6)
(4, 4)
(-4, -6)
(-2, -3)
Obj. 3: 8.6A

4. 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

5. Dilations, cont…
Example: ΔABC ~ ΔMNO is shown below. Which scale factor was used to transform ΔMNO to ΔABC?
ΔMNO
ΔABC
Because our triangle became larger (enlargement) we choose the answer >1 : 5
3.33 : A B C M N O
1 : 5
4.5 3 3 15 15 22
Obj. 3: 8.6A

6. Transformations Four types of Transformations Translation (slide)
Reflection (flip over)
Obj. 3: 8.6AB

7. 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

8. Translations, cont…
Example: ΔDEF is translated 3 units to the right and 3 units down. Which coordinate pair best represents F’?
(4, 2)
(-1, -3)
(3, -6)
(0, -3) D’ F’
Obj. 3: 8.6B

9. 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

10. 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?
(-4, -3)
(-1, -5)
(3, -2)
(1, 5)
(3, -2)
(-4, -3)
(-1, -5)
Obj. 3: 8.6B

11. Views of 3-D Solids
You must be able to imagine a 3-D solid from every angle
Left
Front
Left
Top
Right 1 3 2
Right
Front
Obj. 3: 8.7A

12. 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

13. 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