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Let us consider an example of how to plot a point \((6,5)\) in the cartesian plane:
1. Let us start from the origin \((0,0)\), move \(6\) units along \(OX\).
2. From the point \(6\) in the \(x\) - axis, move \(5\) units parallel to \(OY\) to reach the point \((6,5)\).
Example:
Plot the points \((2,-3)\), \((4,5)\), \((-7,3)\), \((0,3)\) and \((-4,0)\) in the cartesian plane.
Solution:
(\(i\)) To plot \((2,-3)\):
Start from the origin \((0,0)\), move \(2\) units along with \(OX\) and from point \(2\) in the \(x\) - axis move \(3\) units parallel to \(OY'\).
(\(ii\)) Plot \((4,5)\):
Start from the origin \((0,0)\), move \(4\) units along with \(OX\) and from point \(4\) in the \(x\) - axis move \(5\) units parallel to \(OY\).
(\(iii\)) Plot \((-3,3)\):
Start from the origin \((0,0)\), move \(3\) units along with \(OX'\) and from point \(-3\) in the \(x\) - axis move \(3\) units parallel to \(OY\).
(\(iv\)) Plot \((0,3)\):
Since the \(x\) - coordinate is \(0\), and the \(y\) - coordinate is \(3\), the point lies on the \(y\) - axis. Start from \((0,0)\), move \(3\) units along \(OY\).
(\(v\)) Plot \((-4,0)\):
Since the \(x\) - coordinate is \(-4\), and the \(y\) - coordinate is \(0\), the point lies on the \(x\) - axis. Start from \((0,0)\), move \(4\) units along \(OX'\).
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