Math, asked by km3437423, 4 months ago

The angle between the lines x – 2y = y and y – 2x = 5 is​

Answers

Answered by amansharma264
27

EXPLANATION.

Angle between the lines,

⇒ x - 2y = 2.

⇒ y - 2x = 5.

As we know that,

Slope of the line : y = mx + c.

Equation : x - 2y = 2.

⇒ x = 2 + 2y.

⇒ x - 2 = 2y.

⇒ x/2 - 2/2 = y.

Slope = M₁ = 1/2.

Equation : y - 2x = 5.

⇒ y = 5 + 2x.

Slope = M₂ = 2.

As we know that,

Formula of angle between the lines,

⇒ tan∅ = | m₁ - m₂/1 + m₁m₂|

⇒ tan∅ = | 1/2 - 2/1 + (1/2)(2) |.

⇒ tan∅ = | 1 - 4/2/1 + 1 |.

⇒ tan∅ = | -3/2/2 |.

⇒ tan∅ = | -3/4 |.

⇒ tan∅ = 3/4.

⇒ ∅ = tan⁻¹(3/4).

                                                                                                                         

MORE INFORMATION.

(1) = Distance between two parallel lines.

ax + by + c₁ = 0  &  ax + by + c₂ = 0  then,

d = | c₁ - c₂/√a² + b² |.

(2) = Condition of concurrency.

\sf \left[\begin{array}{ccc}a_1&b_1&c_1\\a_2&b_2&c_2\\a_3&b_3&c_3\end{array}\right] = 0

Answered by anshu24497
7

 \huge{\textsf{\textbf{\color{deepskyblue}Answer : }}}

Angle between the lines are :

  • x - 2y = 2.
  • y - 2x = 5.

 \large{ \textsf{ \textbf{ \purple{Explanation}}}}

We know :

• Slope of the line : y = mx + c

Equation : x - 2y = 2

⇒ x = 2 + 2y

⇒ x - 2 = 2y

⇒ x/2 - 2/2 = y

• Slope = M₁ = 1/2

Equation : y - 2x = 5

⇒ y = 5 + 2x

• Slope = M₂ = 2

We know that,

Formula of angle between the lines,

⇒ tan∅ = | m₁ - m₂/1 + m₁m₂|

⇒ tan∅ = | 1/2 - 2/1 + (1/2)(2) |

⇒ tan∅ = | 1 - 4/2/1 + 1 |

⇒ tan∅ = | -3/2/2 |

⇒ tan∅ = | -3/4 |

⇒ tan∅ = 3/4

⇒ ∅ = tan⁻¹(3/4)

                                                                                               

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