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