# if the line L1, passes through the first pair of points, L2 through the second pair, find the angle from L1 to L2. given are; (1,9),(2,6);(3,3),(-1,5) got this ffrom the book analytic geometry by love and rainville and it give me 45 degrees as an answer. how is that?

## Expert Answers You need to remember the equation that helps you to find the angle between the given lines `l_1` and `l_2` , such that:

`tan alpha = (m_1 - m_2)/(1 + m_1*m_2)`

`m_1` represents the slope of the line ` l_1`

`m_2` represents the slope of the line ` l_2`

Since the line l_1 passes through the points `(1,9)` and `(2,6)` yields:

`m_1 = (6 - 9)/(2 - 1) => m_1 = -3`

Since the line `l_2` passes through the points `(3,3)` and `(-1,5)` yields:

`m_2 = (5 - 3)/(-1-3) => m_2 = 2/(-4) => m_2 = -1/2`

You may substitute -`3` for `m_1` and -`1/2` for `m_2` in equation of tangent `alpha` , such that:

`tan alpha = (-3 + 1/2)/(1 + 3/2) => tan alpha = (-5/2)/(5/2) = -1`

You need to remember that the tangent of an angle is negative if the angle is obtuse, hence `alpha = pi - pi/4 = (3pi)/4` or `alpha = 180^o - 45^o = 135^o` .

Hence, evaluating the angle between the lines l_1 and l_2 yields `alpha = (3pi)/4` .

Approved by eNotes Editorial Team

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