Question

The coordinates of a point on the line $x+y=3$ such that the point is at equal distance from the lines $\left|x\right|=\left|y\right|$ are

• A. $(3,0)$
• B. $(0,3)$
• C. $(-3,0)$
• D. $(0,-3)$

Answer 1

Answer: (A), (B)

$(3,0)$
$(0,3)$

$\left|x\right|=\left|y\right|\Rightarrow x-y=0$ and $x+y=0$
Bisector of angle between these lines are
$\frac{x-y}{\sqrt{2}}=\pm \frac{x+y}{\sqrt{2}}\Rightarrow x=0$ and $y=0$
By solving $x=0$ and $x+y=3\Rightarrow (0,3)$
and solving $y=0$ and $x+y=3\Rightarrow (3,0)$