Question

Given the line $3x+5y=15$ and a point on this line equidistant from the coordinate axes. Such a point exists in:

none of the quadrants

quadrant $\mathrm{I}$ only

quadrants $\mathrm{I},$ $\mathrm{II}$ only

quadrants $\mathrm{I},$ $\mathrm{II},$ $\mathrm{III}$ only

each of the quadrants

Answer: C

Concepts:coordinate geometry absolute value system of equations

Difficulty rating: 1210

Small Hint:

A point equidistant from the axes satisfies $|x|=|y|$

Big Hint:

Intersect the given line with both $y=x$ and $y=-x$

Solution:

For $y=x,$ the line gives $8x=15,$ producing a point in quadrant I. For $y=-x,$ it gives $-2x=15,$ so $x\lt0$ and $y>0,$ producing a point in quadrant II. There are no other possibilities.

Therefore, the correct answer is C.

1960 AMC 12 Problem 30

Answer: C

Difficulty rating: 1210

Small Hint:

Big Hint:

Solution:

Problem 30 in Other Years