1)How many different lines of symmetry does a regular 11-gon have?

Picture: https://latex.artofproblemsolving.com/8/4/4/84445c7f96e3f03517a1e8c2b67725eb69bfc74e.png


2)Point Q is the image of point P under a dilation with center O and scale factor 4. If PQ = 18, then what is OP?


3)A reflection maps A to B and B to C. Given AB = 12 find AC.


4)A dilation with scale factor -3 maps X to Xprime and Y to Yprime. Given XprimeYprime = 2, find XY.


5)A reflection maps A to B and C to C. If AB = 12, then what is the shortest possible length of AC?


6)When a square with area 4 is dilated by a scale factor of k we obtain a square with area 9. Find the sum of all possible values of k.


7)In triangle ABC, AB = BC = 5 and CA = 6.

 Triangle ABC is first rotated clockwise about A for 90 degrees to triangle AB1C1.
  Triangle AB1C1 is then reflected over B1C1 to triangle A1B1C1.
   Triangle A1B1C1 is then translated 8 units to the right to triangle A2B2C2.
    Triangle A2B2C2 is then dilated about A to triangle A3B3C3 with scale factor -4.
     What is the perimeter of triangle A3B3C3?

Picture: https://latex.artofproblemsolving.com/e/6/9/e69e279ed1f8312a80941122afbf3d2a8b6b119a.png


8)D, E and F are the midpoints of BC, CA, and AB respectively. A dilation maps triangle ABC to triangle DEF. What is the scale factor of this dilation?

Picture: https://latex.artofproblemsolving.com/2/7/7/277eb9ff33baa2ebc2195fb52a18918053f002e0.png


9)In triangle XYZ, XY = 20, YZ = 15 and XZ = 25. Y is reflected over XZ to Yprime. Find YYprime.

Picture: https://latex.artofproblemsolving.com/4/7/d/47deb1d8e00693fe83789bc760cf9f4cef5a5013.png


10)As shown in the diagram, angle MOL = 30 degrees and A is a point inside angle MOL with OA = 6. Let B and C be points on rays OM and OL, respectively. Find the smallest possible perimeter of triangle ABC.

Picture: https://latex.artofproblemsolving.com/7/d/9/7d957ed179a1092b65680707dd356a356d05a02e.png


11)A laser is shot from vertex A of square ABCD of side length 1, towards point P on BC so that BP = 3/4. The laser reflects off the sides of the square, until it hits another vertex, at which point it stops. What is the length of the path the laser takes?

Picture: https://latex.artofproblemsolving.com/c/9/0/c904b038f475065d64d6dbc320b079311b9b2d2b.png 

FiestyGeco  Apr 29, 2018

Why do you always post the AoPS class questions for Geometry just so that you can get the answers? What is the point of even taking the class then?!

Guest May 12, 2018

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