If `A(-2,1),B(2,3)a n dC(-2,-4)` are three points, find the angle between `A Ba n dB Cdot`

Explanation

Let the slope of line `A B` and `B C` be `m_{1}` and `m_{2}` respectively.

As we have know that slope of line joining points `(x_{1}, y_{1})` and `(x_{2}, y_{2})` is given by`{m}=frac{({y}_{2}-{y}_{1})}{({x}_{2}-{x}_{1})}`

Therefore,

`{m}_{1}=frac{(3-1)}{(2-(-2))}=frac{1}{2}`

`{~m}_{2}=frac{((-4)-3)}{((-2)-2)}=frac{7}{4}`

Let `theta` be the angle between the lines `A B` and `A C`.

`therefore tan theta=frac{m_{2}-m_{1}}{1+m_{2} m_{1}}`

`Rightarrow tan theta=frac{(frac{7}{4})-(frac{1}{2})}{1+(frac{7}{4})(frac{1}{2})}`

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