Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ 2 2 2 k cos 2 k s k k k 2 2 2 2 2 2 2 2 2 in cos cos 2k sin 2 cos 2sin 2 Hence, we proved that 2 p 4q k 2 2 2 Question 17: In the triangle ABC with vertices A (2, 3), B(4, -1) and C(1, 2), find the equation and length of altitude from the vertex A. Solution 17: Let AD be the altitude of triangle ABC from vertex A. Accordingly, ADBC The equation of the line passing through point (2, 3) and having a slope of 1 is (y – 3) = 1(x – 2) x y1 0 y x1 Therefore, equation of the altitude from vertex A = y – x = 1. Length of AD = Length of the perpendicular from A (2, 3) to BC The equation of BC is 21 y1 x4 14 y1 1 x4 y1 x 4 x y3 0 ... 1 The perpendicular distance (d) of a line Ax + By + C = 0 from a point x y is given by 1, 1 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ d Ax By C 1 1 2 2 A B On comparing equation (1) to the general equation of line Ax + By + C = 0, we obtain A = 1, B = 1, and C = -3. 12+1 3-3 2 2 Length of AD = units units units 2units 2 2 1 1 2 2 Thus, the equation and length of the altitude from vertex A are y – x = 1 and respectively. 2 units Question 18: If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a, and b, then show that 1 1 1 2 2 2 p a b Solution 18: It is known that the equation of a line whose intercepts on the axes are a and b is x y 1 a b Or bx + ay = ab Or bx + ay – ab = 0 …(1) The perpendicular distance (d) of a line Ax + By + C = 0 from a point x y is given by d Ax By C 1 1 2 2 A B On comparing equation (1) to the general equation of line Ax – By + C = 0, we obtain A = b, B = a, and C = -ab. Therefore, if p is the length of the perpendicular from point x y = (0, 0) to line (1), We obtain A(0) B 0 ab p 2 2 b a ab p 2 2 b a On squaring both sides, we obtain 1, 1 1, 1 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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