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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 \(OX\) and from the 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 \(OX\) and from the 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 \(OX'\) and from the 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 \(OX'\).