Parallel and perpendicular lines


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Let l1 and l2 be any two lines intersecting at P.

Let line l1 be inclined at an angle q1 and line l2 be inclined at an angle q2 with the x-axis in the positive direction.

Let f be the angle between the lines.

m1 = slope of line l1, m2 = slope of line l2

From the figure,

Parallel lines

l1 is parallel to l2 if f = 900.

\Two lines are parallel if their slopes are equal.

Perpendicular lines

Two lines are perpendicular if the product of their slopes is -1 or slope of one line is the negative reciprocal of the other i.e., 

Example:

Show that the line through (-6,6) and (-1,-3) is perpendicular to the line through (2,-4) and 

Suggested answer:

Since, the product of the slopes = -1, the lines are perpendicular to each other.


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