Problem: Given the line and a point on this line equidistant from the coordinate axes. Such a point exists in:
Answer Choices:
A. none of the quadrants
B. quadrant I only
C. quadrants I, II only
D. quadrants I, II, III only
E. each of the quadrants
Solution:
The locus of points equidistant from the coordinate axes is the pair of lines and .
Solve simultaneously and to obtain . The point in quadrant , therefore, satisfies the required condition.
Solve simultaneously and to obtain . The point in quadrant , therefore, satisfies the required condition.
There are no other solutions to these pairs of equations, and, therefore, no other points satisfying the required condition.