The point whose abscissa is equal to its ordinate and which is equidistant from the points $(1, 0)$ and $(0, 3)$ is

If a point $P$ on the line $3x + 5y = 15$ is equidistant from the coordinate axes,then $P$ lies

If two mutually perpendicular lines through the point $A(1, 1)$ intersect the $x$-axis and $y$-axis at points $B$ and $C$ respectively,then the locus of the centroid of $\Delta ABC$ is -

$A$ variable line passes through a fixed point $P$. If the algebraic sum of the perpendiculars drawn from $(2, 0)$,$(0, 2)$,and $(1, 1)$ to the line is zero,then the coordinates of the point $P$ are:

$A$ straight line passes through a fixed point $(h, k)$. The locus of the foot of the perpendicular drawn from the origin to this line is:

$A$ point on the straight line $3x + 5y = 15$ which is equidistant from the coordinate axes will lie in