### Theory:

• Co-ordinates are ordered pairs used to represent the position of a point in the cartesian plane.
• The terms $$(x, y)$$, $$(-x, y)$$, $$(-x,-y)$$, $$(x,-y)$$ are called co-ordinates which are used to locate the position of a point in the quadrants $$I$$, $$II$$, $$III$$ and $$IV$$ respectively in a cartesian plane.
• $$x$$-co-ordinate of a point:

The $$x$$-coordinate of a point is the perpendicular distance from the $$y$$-axis measured along the $$x$$-axis.

$$y$$-co-ordinate of a point:

The $$y$$-coordinate of a point is the perpendicular distance from the $$x$$-axis measured along the $$y$$-axis.

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 and 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 at the first quadrant in the above graph; hence its co-ordinates will be represented as $$(x, y)$$, where $$x=3$$ and $$y=4$$ is the co-ordinate of $$L$$ in cartesian plane is represented as $$(3,4)$$.

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 and 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 at the second quadrant in the above graph; hence its co-ordinates will be represented as $$(-x, y)$$, where $$x=4$$ and $$y=2$$ is the co-ordinate of $$M$$ in cartesian plane is represented $$(-4,2)$$.

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 and 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 at the third quadrant in the above graph; hence its co-ordinates will be represented as $$(-x, -y)$$, where $$x=2$$ and $$y=3$$ is the co-ordinate of $$L$$ in cartesian plane is represented as $$(-2,-3)$$.

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 and 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 at the fourth quadrant in the above graph; hence its co-ordinates will be represented as (x, -y), where $$x=1$$ and $$y=3$$ is the co-ordinate of $$L$$ in cartesian plane is represented as $$(1,-3)$$.
Important!
Measure the positive coordinate value along the positive direction of the axis and the negative coordinate value along the negative direction of the axis.