Coordinate Geometry - Identifying Quadrants

In coordinate geometry, we use two coordinate axes (the $x$-axis and $y$-axis) to identify the location of any point.

$(3, 5)$ is the location of a point having location $3$ on the $x$-axis and location $5$ on the $y$-axis. That is, the first number is the $x$-coordinate, and the second number is the $y$-coordinate.

The perpendicular distance of a point from the $y$-axis is called the $x$-coordinate. Similarly, the perpendicular distance of a point from the $x$-axis is called the $y$-coordinate.

The intersection of the $x$-axis and $y$-axis divides the plane into four quadrants.

On the $x$-axis the positive numbers run to the right, while the negative numbers run to the left. Similarly, on the $y$-axis the positive numbers run upwards, while the negative numbers run down.

The coordinate plane has two axes: the horizontal and vertical axes. These two axes intersect each other at a point called the origin. It can also be defined as the $(0,0)$ point in the coordinate plane.

Suppose we need to find the quadrant of a point $(x,y)$.

• If both $x$ and $y$ are positive, then the point lies in the first quadrant.
• If $x$ is negative and $y$ is positive, then the point lies in the second quadrant.
• If both $x$ and $y$ are negative, then the point lies in the third quadrant.
• If $x$ is positive and $y$ is negative, then the point lies in the fourth quadrant.

These are often numbered from $1^\text{st}$ to $4^\text{th}$ and denoted by Roman numerals: I $($where the signs of the two coordinates are (+,+)$)$, II (−,+), III (−,−), and IV (+,−).

Find the quadrant in which the point $(-5,11)$ lies.

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As the $x$-coordinate is negative and the $y$-coordinate is positive , the point lies in the second quadrant. $_\square$

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