### Theory:

1. The perpendicular distance of the point $$L$$ from the $$y$$ - axis measured along the positive direction of the $$y$$-axis is $$LX = 4$$ units. The perpendicular distance of the point $$L$$ from the $$x$$-axis measured along the positive direction of the $$x$$- axis $$OL = 3$$ units.
Point L lies in first quadrant in the above graph. Hence its co-ordinates will be represented as (x, y), where $$x = 3$$ and $$y = 4$$ the co-ordinate of $$L$$ in cartesian plane is $$(3,4)$$.

2. The perpendicular distance of the point $$M$$ from the $$y$$ - axis measured along the positive direction of the $$y$$-axis is $$MX' = 2$$ units. The perpendicular distance of the point $$M$$ from the x-axis measured along the negative direction of the $$x$$ - axis $$OM = 2$$ units.
Point M lies in second quadrant in the above graph. Hence its co-ordinates will be represented as (-x, y), where $$x = 4$$ and $$y = 2$$ the co-ordinate of M in cartesian plane is $$(-4,2)$$.

3. The perpendicular distance of the point $$N$$ from the $$y$$ - axis measured along the negative direction of the $$y$$-axis is $$NX' = 3$$ units. The perpendicular distance of the point $$N$$ from the $$x$$-axis measured along the negative direction of the $$x$$ - axis $$OX' = 2$$ units.
Point N lies in third quadrant in the above graph. Hence its co-ordinates will be represented as (-x, -y), where $$x = 2$$ and $$y = 3$$ the co-ordinate of $$L$$ in cartesian plane is $$(-2,-3)$$.

4. The perpendicular distance of the point $$Q$$ from the $$y$$ - axis measured along the negative direction of the y-axis is $$QX' = 3$$ units. The perpendicular distance of the point $$Q$$ from the $$x$$-axis measured along the positive direction of the $$x$$ - axis $$OX = 1$$ unit.
Point $$Q$$ lies in fourth quadrant in the above graph. Hence its co-ordinates will be represented as (x, -y), where $$x = 1$$ and $$y = 3$$ the co-ordinate of $$L$$ in cartesian plane is $$(1,-3)$$.