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Quadrants:
- The \(x\)-axes and \(y\)-axes divided the cartesian plane into four infinite regions with equal distance from the origin and bordered by two axes.
- These are called quadrants. Quadrants divide the cartesian plane into \(4\) equal parts. They are usually numbered in anticlockwise direction starting from the region bounded by positive \(x\) and \(y\)-axis (that is \(OX\)).
Quadrant I:
- Any point located in quadrant \(I\) will have a positive number in the \(x\)-axis and \(y\)-axis.
- It can be represented as \(( x, y)\), where \(x\) and \(y\) represent the distance of a point from the origin horizontally and vertically.
Example:
\((2,3)\), \((6,10)\), \((9,12)\)
Quadrant II:
- Any point located in quadrant \(II\) will have a negative number in the \(x\)-axis and positive number in \(y\)-axis.
- It can be represented as \((-x, y)\), where \(x\) and \(y\) represent the distance of the point from the origin horizontally and vertically.
Example:
\((-3,6)\), \((-2,5)\), \((-15,12)\)
Quadrant III:
- Any point located in quadrant \(III\) will have a negative number in the \(x\)-axis and \(y\)-axis.
- It can be represented as \(( -x, -y)\), where \(x\) and \(y\) represent the distance of the point from the origin horizontally and vertically.
Example:
\((-5,-6)\), \((-2,-1)\), \((-8,-10)\)
Quadrant IV:
- Any point located in quadrant \(IV\) will have a positive number in the \(x\)-axis and negative number in \(y\)-axis.
- It can be represented as \((x, -y)\), where \(x\) and \(y\) represent the distance of the point from the origin horizontally and vertically.
Example:
\((1,-3)\), \((3, -4)\), \((7,-1)\)
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