anonymous
  • anonymous
NVM
Mathematics
chestercat
  • chestercat
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Directrix
  • Directrix
@superraymond Lengths of corresponding sides of similar polygons are in proportion (by definition of similar polygons). So the following extended proportion is true: (x - 1) / 6 = (y+1)/21 = 32/24 = 16/12
Directrix
  • Directrix
Of those, the last two simplify to 4/3 which is the scale factor. To find x, solve for x in this proportion, (x - 1) / 6 = 4/3 -- > Read as (x - 1 ) is to 6 as 4 is to 3. Use the means-extremes property (cross multiply). 3*(x - 1) = 6*4 What comes next?
Directrix
  • Directrix
I understand that you feel lost right off the bat but I have to ask if you know the definition of similar polygons. In Geometry, there's no getting around learning the theorems and the definitions.

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Directrix
  • Directrix
I am asking you to solve 3*(x - 1) = 6*4 for x.
Directrix
  • Directrix
Use the Distributive Property to multiply 3 times BOTH x and -1. 3*(x-1)= 3x-1 is not correct. Try again.
Directrix
  • Directrix
Correct. Do you want to find y?
Directrix
  • Directrix
I am not sure which 3 and 4 you mean. Is it this --> the last two simplify to 4/3
Directrix
  • Directrix
Lengths of corresponding sides of similar polygons are in proportion. That means this: (x - 1) / 6 = (y+1)/21 = 32/24 = 16/12 Look at 32/24 = 16/12 --> Both simplify to 4/3 or 4 to 3. The ratio of corresponding sides is 4 to 3. That is why (x - 1) / 6 = 4/3. (y+1)/21 is also equal to 4/3.
Directrix
  • Directrix
Instead of 4/3, you could use 16/12 or 32/24 to solve for x. The answer would be the same because both 16/12 and 32/24 = 4/3.
Directrix
  • Directrix
Glad to help.

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