A point lying on the line 3x + 5y = 15 that is equidistant from both coordinate axes can only exist in which quadrant(s)?

1st and 2nd quadrants
4th quadrant
1st, 2nd and 4th quadrants
1st quadrant only

Correct answer: 1st and 2nd quadrants

Solution

Points equidistant from both coordinate axes lie on y = x or y = -x. Substituting y = x gives (15/8, 15/8) in Q1; substituting y = -x gives (-15/2, 15/2) in Q2. So only Q1 and Q2 are possible.

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