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Washington State Math Olympiad
Hints and Solutions
2015 Grade 8 Geometry
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Hint |
1) In the diagram shown, what is the angle of VAB?
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- Angle ACB is vertical with angle YCZ, so it is _____ degrees.
- Angle ABC is vertical with angle WBX, so it is _____ degrees.
- Angle BAC is _____ degrees.
- Angle VAB is supplementary with angle BAC and is therefore _____ degrees.
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2) A data set consists of seven different positive whole numbers. The mean of the data is 76. What is the largest possible median of the data?
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- For the median to be maximum, the 3 numbers below it must be as small as possible =
___, ___, and ___
- The 7 members of the data set must sum to _____ so the median and the 3 numbers above it must sum to _____
- For the median to be maximum, the median and the 3 numbers above it must be as high as possible, so if they are all different they must be ____, ____, ____ and ____, so the highest median is _____
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3) Rotate triangle XYZ 90 degrees clockwise (↷) about point Y. What will the translated coordinates of point Z be?)
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- Point Y is (___,___)
- Translate the entire triangle to make point Y the origin:
The translated point Z = (___, ___)
- To rotate a point (a,b) clockwise 90 degrees, it's new coordinates become (b,-a)
- Translated, rotated Z point = (___,___)
- Translate Z back into original coordinates:
Original Z rotated 90 degrees clockwise =
(___, ___)
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