Difference between revisions of "1996 AJHSME Problems/Problem 17"
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Figure <math>OPQR</math> is a square. Point <math>O</math> is the origin, and point <math>Q</math> has coordinates (2,2). What are the coordinates for <math>T</math> so that the area of triangle <math>PQT</math> equals the area of square <math>OPQR</math>? | Figure <math>OPQR</math> is a square. Point <math>O</math> is the origin, and point <math>Q</math> has coordinates (2,2). What are the coordinates for <math>T</math> so that the area of triangle <math>PQT</math> equals the area of square <math>OPQR</math>? |
Revision as of 19:47, 10 November 2012
Problem
Figure is a square. Point is the origin, and point has coordinates (2,2). What are the coordinates for so that the area of triangle equals the area of square ?
Solution
The area of is .
The area of is .
If we set the areas equal, the area of $\traingle PQT$ (Error compiling LaTeX. Unknown error_msg) is . Also, note that . Plugging those in, we get:
If , and , then , and must be units to the left of the origin. This would be , giving answer .
See Also
1996 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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 AJHSME/AMC 8 Problems and Solutions |