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# Can someone help me with this, If A(-2,1), B(2,3) and C(-2,-4) are three points, then the angle between BAand BC is

If A(-2,1), B(2,3) and C(-2,-4) are three points, then the angle between BA and BC is

• Option 1)

$\tan ^{-1}\left ( \frac{3}{2} \right )$

• Option 2)

$\tan ^{-1}\left ( \frac{2}{3} \right )$

• Option 3)

$\tan ^{-1}\left ( \frac{7}{4} \right )$

• Option 4)

None

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Angle between two lines (?) -

$\tan \Theta = \frac{m_{2}-m_{1}}{1+m_{1}m_{2}}$

- wherein

Here $m_{1},m_{2}$ are the slope of two lines

$m_{1}=\frac{3-1}{2+2}=\frac{1}{2}$

$m_{2}=\frac{3+4}{2+2}=\frac{7}{4}$

$\tan \theta = \frac{\frac{1}{2}-\frac{7}{4}}{1+\frac{1}{2}\times \frac{7}{4}}$

$\frac{-10}{8+7}=\frac{-10}{15}=\frac{-2}{3}$

So, acute angle $\tan ^{-1}\left ( \frac{2}{3} \right )$

Option 1)

$\tan ^{-1}\left ( \frac{3}{2} \right )$

This solution is incorrect

Option 2)

$\tan ^{-1}\left ( \frac{2}{3} \right )$

This solution is correct

Option 3)

$\tan ^{-1}\left ( \frac{7}{4} \right )$

This solution is incorrect

Option 4)

None

This solution is incorrect

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