Question

Find the angle between lines l1 with slope -7 and line l2 which passes through (2, -1) and (5,3)

Answer 1

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Answer:

$\boxed{\sf The \ angle \ between\ them \ is \ 45^{\circ}}$

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Step-by-step explanation:

Given that , the slope of line l₁ is 7 and the line l₂ passes through two points. We can find the slope of the second line as ,

$\sf\dashrightarrow Slope = \dfrac{ y_2-y_1}{x_2-x_1} \\\\\sf\dashrightarrow m_2 = \dfrac{ 3 + 1}{5-2} \\\\\sf\dashrightarrow \boxed{\red{\sf m_2 = \dfrac{4}{3} }}$

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Let the slope of line l₁ be m₁ = 7 and that of line l₂ be m₂ = 4/3 . Now we know that , if two lines have their slopes as m₁ and m₂ , then the angle between them is given by ,

$\sf\dashrightarrow tan\theta = \dfrac{ m_1-m_2}{1 + m_1 m_2} \\\\\sf\dashrightarrow tan\theta = \dfrac{ -7 - \dfrac{4}{3}}{1+(-7)\bigg( \dfrac{4}{3}\bigg)} \\\\\sf\dashrightarrow tan\theta = \dfrac{ \dfrac{- 25}{3}}{1-\dfrac{ 28}{3}} \\\\\sf\dashrightarrow tan\theta = \dfrac{ \dfrac{-25}{3}}{\dfrac{ 3-28}{3}} \\\\\sf\dashrightarrow tan\theta =\dfrac{\dfrac{-25}{3}}{\dfrac{-25}{3}} \\\\\sf\dashrightarrow tan\theta = 1\\\\\sf\dashrightarrow \theta = tan^{-1}(1) \\\\\sf\dashrightarrow \boxed{\pink{\frak{ \frak{ \theta = 45^{\circ}}}}}$

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