Straight Line and Pair of Straight Lines 1 Question 9
9. A point on the straight line, $3 x+5 y=15$ which is equidistant from the coordinate axes will lie only in
(2019 Main, 8 April I)
(a) IV quadrant
(b) I quadrant
(c) I and II quadrants
(d) I, II and IV quadrants
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Solution:
- Given equation of line is $3 x+5 y=15$
Clearly, a point on the line (i), which is equidistance from $X$ and $Y$-axes will lie on the line either $y=x$ or $y=-x$.
In the above figure, points $A$ and $B$ are on the line (i) and are equidistance from the coordinate axes.
On solving line (i) and $y=x$, we get $A \frac{15}{8}, \frac{15}{8}$.
Similarly, on solving line (i) and $y=-x$, we get B $-\frac{15}{2}, \frac{15}{2}$.
So, the required points lie only in I and II quadrants.
