– α ) tan tan tan tan m m m m α α α α (as + m m ≠ ) and φ = ° – θ so that tan φ = tan ( ° – θ ) = – tan θ = – m m m m , as + m m ≠ Fig . Now, there arise two cases: STRAIGHT LINES Case I If – m m m m i s positive, then tan θ will be positive and tan φ will be negative, which means θ will be acute and φ will be obtuse. Case II If – m m m m is negative, then tan θ will be negative and tan φ will be positive, which means that θ will be obtuse and φ will be acute. Thus, the acute angle (say θ ) between lines L and L with slopes m and m , respectively, is given by tan θ , as m m m m m m ≠ ...
( ) The obtuse angle (say φ ) can be found by using φ = – θ . Example If the angle between two lines is π and slope of one of the lines is , find the slope of the other line. Solution We know that the acute angle θ between two lines with slopes m and m is given by tan θ m m m m ... ( ) Let m = , m = m and θ = π .
Now, putting these values in ( ), we get π tan or m m , m m which gives or m m – . m m Therefore or m m = − MATHEMATICS Fig . Hence, slope of the other line is or . Fig .
explains the reason of two answers. Fig . Example Line through the points (– , ) and ( , ) is perpendicular to the line through the points ( ,