# 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?

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` .

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