What is the angle between the lines whose equations are: 3x + y – 7 = 0 and x + 2y + 9 = 0. -Maths 9th

What is the angle between the lines whose equations are: 3x + y – 7 = 0 and x + 2y + 9 = 0. -Maths 9th
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(c) (8, 6)Let AB be the given line 4x + 3y = 25 Let O′(a, b) be the image of O in the given line AB. Let O O′ cut AB in point P. Also OP ⊥ AB and P is the mid-point of OO′. ∴ Co-ordinates of P are \(\bigg(rac{a}{2},rac{b}{2}\bigg)\)∵ P lies on AB \(4 imesrac{a}{2}+3 imesrac{b}{2}-25=0\)⇒ 4a + 3b = 50                          ...(i) Also, OO′ ⊥ AB ⇒ slope of OO′ x slope of AB = –1⇒ \(\big(rac{b-0}{a-0}\big)\) x \(rac{-4}{3}\) = -1          \(\big(\because ext{Line}\,AB : y =rac{-4x}{3}+rac{25}{3}\big)\)⇒ \(rac{b}{a}\) = \(rac{4}{3}\) ⇒ 3a = 4bFrom (ii), a = \(rac{4a}{3}\). Putting this value of a in (i), we get4 x \(rac{4a}{3}\) + 3b = 50⇒ 16b + 9b = 150 ⇒ 25b = 150 ⇒ b = 6⇒ a = \(rac{4 imes6}{3}\) = 8∴ The image of the point O(0, 0) in the line 4x + 3y – 25 = 0 is (8, 6).
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