Warm Up Simplify each radical. 1. 2. 3. Find the distance between each pair of points. Write your answer in simplest
radical form. 4. C (1, 6) and D (2, 0) 5. E(7, 1) and F(1, 5) Objectives Apply similarity properties in the coordinate plane. Use coordinate proof to prove figures similar.
Vocabulary dilation scale factor A dilation is a transformation that changes the size of a figure but not its shape. The preimage and the image are always similar.
Scale Factor the ratio of image to its pre-image The ratio of corresponding sides Scale Factor When scale factor is greater than 1, the shape gets bigger
(enlargement). When scale factor is less than 1, but greater than 0, the shape gets smaller (reduction). SCALE FACTOR. 6
2 B A 14 6 3
2 1 C 6 1 0 7
D 3 5 5 1 10 2
Find the coordinates of the dilation image for the given scale factor, k. Example 1: G(0, -2), H(1, 3), and I(4, 1); k = 2 All you do is multiply k to
(x, y). G( , ), H( , ), and I( , ) Find the coordinates of the dilation image for the given scale factor, k. Example 2: L(8, -8), N(0, 16), and M(4, 5); k = 1/4
All you do is multiply k to (x, y). L( , ), N( ,
), and M( , ) k = 1/2 k=2
Example 1: Computer Graphics Application Draw the border of the photo after a dilation with scale factor Example 1 Continued Step 1 Multiply the vertices of the photo A(0, 0), B(0, 4), C(3, 4), and D(3, 0) by Rectangle
ABCD Rectangle ABCD Example 1 Continued Step 2 Plot points A(0, 0), B(0, 10), C(7.5, 10), and D(7.5, 0). Draw the rectangle.
Example 2: Finding Coordinates of Similar Triangle Given that TUO ~ RSO, find the coordinates of U and the scale factor. Since TUO ~ RSO, Substitute 12 for RO, 9 for TO, and 16 for OY.
12OU = 144 OU = 12 Cross Products Prop. Divide both sides by 12. Example 2 Continued U lies on the y-axis, so its x-coordinate is 0. Since OU = 12, its y-coordinate must be 12. The coordinates of
U are (0, 12). So the scale factor is Check It Out! Example 2 Given that MON ~ POQ and coordinates P (15, 0), M(10, 0), and Q(0, 30), find the coordinates of N and the scale factor.
Since MON ~ POQ, Substitute 10 for OM, 15 for OP, and 30 for OQ. 15 ON = 300 ON = 20 Cross Products Prop. Divide both sides by 15.
Check It Out! Example 2 Continued N lies on the y-axis, so its x-coordinate is 0. Since ON = 20, its y-coordinate must be 20. The coordinates of N are (0, 20). So the scale factor is Lesson Quiz: Part I
1. Given X(0, 2), Y(2, 2), and Z(2, 0), find the coordinates of X', Y, and Z' after a dilation with scale factor 4. X'(0, 8); Y'(8, 8); Z'(8, 0) 2. JOK ~ LOM. Find the coordinates of M and the scale factor. Lesson Quiz: Part II 3. Given: A(1, 0), B(4, 5), C(2, 2), D(2, 1), E(4, 9), and F(8, 3)
Prove: ABC ~ DEF Therefore, by SSS ~. and ABC ~ DEF
Implementing PPM and PM Methodologies. Created an evaluation form that team members could use to score projects against the criteria contained in the initial proposal template. Used a scoring scale of 0, 1, 3, 9 to perceived indicate degree of...
Types of Bills. Bills. P_____ P_____ Riders - Open bill with additions that have nothing to do with the original bill. Christmas Tree Bills. Why do lawmakers agree to allow riders to be added to their bill? $ Horny Toad...
Peristalsis waves of muscle contractions- pushes food through the to the stomach Stomach J- shaped, muscular pouch Pepsin & Protease enzyme digests proteins Hydrochloric Acid strong acid helps protease, kills bacteria Mucus coats and protects the lining of the stomach...
La signatura electrònica permet donar fiabilitat als tràmits que l'empresa fa a Internet. La signatura electrònica està protegida per certificats electrònics, que són documents que relacionen les claus de la signatura electrònica amb la seva identitat. 16/07/2012. M7-UF1-T2--INSTALACIO I ACTUALITZACIÓ...
19 lines. 5 tercets (three line stanzas) 1 quatrain (four-line stanza) Lines 1 and 3 of first tercet are repeated. Alternate in last lines of next four stanzas. Become two concluding lines in final stanza. Interesting Facts: Villanelles didn't start...
Addition and Subtraction of Radicals You can add and subtract radicals also. However, them must have the same number inside the radicals and can not be added with numbers without radicals. Remember! You can't add radicals with whole numbers! Multiplication...
What are some of the techniques that Priestley uses to present his characters and his central themes in AIC? ... built around analysis of 1 or 2 quotes from the speech. ... Eva Smith= working class women, John Smiths =...
Ready to download the document? Go ahead and hit continue!