Difference between revisions of "1960 AHSME Problems/Problem 30"
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==See Also== | ==See Also== | ||
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Latest revision as of 18:13, 17 May 2018
Problem
Given the line 
and a point on this line equidistant from the coordinate axes. Such a point exists in:
Solution
If a point is equidistant from the coordinate axes, then the absolute values of the x-coordinate and y-coordinate are equal. Since the point is on the line , find the intersection point of 
and and the intersection point of 
and .
Substituting 
for 
in results in 
, so 
. That means 
, so one of the points is in the first quadrant.
Substituting 
and in results in 
, so 
. That means 
, so the other point is in the second quadrant.
Thus, the points are in quadrants 
and 
, so the answer is 
.
See Also
| 1960 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 29 |
Followed by Problem 31 | |
| 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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
