Question

find the equation of the line through ( -2,1) in symmetrical forms when the angle made by the line with positive direction of x axis is 45degree​

Answer 1

EXPLANATION.

Equation of the line through (-2,1) in the symmetric form by the line with positive x-axis = 45°.

Slope of the line = tan∅ = 45°.

Slope of the line = tan∅ = 1.

Equation of the line,

⇒ ( y - y₁) = m ( x - x₁).

⇒ ( y - 1) = 1 ( x -(-2)).

⇒ ( y - 1 ) = 1 ( x + 2 ).

⇒ y - 1 = x + 2.

⇒ y - x = 3.

                                 

MORE INFORMATION.

NOTES.

(1) = Equation of a line which is parallel to ax + by + c is ⇒  ax + by + k.

(2) = Equation of a line which is perpendicular to ax + by + c = 0 is ⇒ bx - ay + k = 0.

The value of k in both cases is obtained with the help of additional information given in the problem.