Question

5. If A(-2, 1), B(2, 3) and C(-2,-4) are three points, find the angle between the lines AB and
ВС.
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Answer 1

Answer:

$\alpha \: is \: the \: required \: angle \\ where \: \cos( \alpha ) = \frac{49}{20 \sqrt{13} }$

Step-by-step explanation:

$a = \sqrt{( {2 + 2)}^{2} + ( {3 + 4)}^{2} } = \sqrt{65} \\ b = \sqrt{( { - 2 + 2)}^{2} + ( {1 + 5)}^{2} } = 6\\ c = \sqrt{( {2 + 2)}^{2} + ( {3 - 1)}^{2} } = 2 \sqrt{5} \\ \cos( \alpha ) = ( {a}^{2} + {c}^{2} - {b}^{2}) \div 2ac \\ \\ \cos( \alpha ) = \frac{49}{20 \sqrt{13} }$