Position of Two Points with Respect to a Given Line
Introduction:
 Understanding the position of points relative to a line is essential in coordinate geometry.
 It involves determining whether points lie on the line, on the same side, or on different sides concerning the given line.
PointPosition Relation to a Line:

On the Line:
 A point (x, y) is on the line if it satisfies the equation of the line when substituted into the equation.

Above or Below the Line:
 Substituting a point's coordinates into the line equation determines whether the point lies above or below the line.
 If the substituted point yields a positive value in the equation, it lies above the line; otherwise, it lies below.

Side Determination using Inequality:
 Given a line equation $Ax+By+C=0$, substitute the point coordinates into the equation: $Ax+By+C>0$ or $Ax+By+C<0$.
 If the inequality is true, the point is on the respective side of the line; if false, it's on the opposite side.
Example:
Consider the line $3x4y+5=0$ and two points:
 Point A(2, 3)
 Point B(1, 6)
Position of Points with Respect to the Line:

Point A(2, 3):
 Substitute into the line equation: $3(2)4(3)+5=612+5=1<0$
 Conclusion: Point A is below the line.

Point B(1, 6):
 Substitute into the line equation: $3(1)4(6)+5=324+5=16<0$
 Conclusion: Point B is below the line.
Importance:
 Understanding the pointline relationship aids in geometric analysis and problemsolving involving regions, distances, or orientations in a coordinate plane.
 This knowledge is essential in fields like computer graphics, engineering, and architecture for determining positions of objects concerning reference lines.
Summary:
 Determining the position of points concerning a line involves substituting their coordinates into the line equation and analyzing the result (equality or inequality).
 This analysis helps establish whether points lie on the line, above, or below it, providing crucial spatial information.