Difference between revisions of "2013 AMC 12B Problems/Problem 8"
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Revision as of 08:58, 7 April 2013
Problem
Line has equation and goes through . Line has equation and meets line at point . Line has positive slope, goes through point , and meets at point . The area of is . What is the slope of ?
Solution
Line has the equation when rearranged. Substituting for ,we find that line will meet this line at point , which is point B. We call the base and the altitutde from A to the line connecting B and C, , the height. The altitude has length , and the area of . Since , . Because has positive slope, it will meet to the right of , and the point to the right of is . passes through and , and thus has slope .
See also
2013 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 7 |
Followed by Problem 9 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |