Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ 3( y1) 5( x1) 3y3 5x 5 i. e.,5x 3y 2 0 Question 8: Find the equation of the line which is at a perpendicular distance of 5 units from the origin and the angle made by the perpendicular with the positive x-axis is 30 . Solution 8: If p is the length of the normal from the origin to a line and is the angle made by the normal with the positive direction of the x-axis, then the equation of the line given by x cos + y sin = p. Here, p = 5 units and = 30 Thus, the required equation of the given line is x cos 30 + y sin 30 = 5 3 1 x y . 5 2 2 i.e., 3xy10 Question 9: The vertices of PQR are P (2, 1), Q (-2, 3) and R (4, 5). Find equation of the median through the vertex R. Solution 9: It is given that the vertices of PQR are P (2, 1), Q (-2, 3) and R (4, 5). Let RL be the median through vertex R. Accordingly, L be the mid-point of PQ. 22 13 By mid-point formula, the coordinates of point L are given by , 0,2 2 2 It is known that the equation of the line passing through points x y , 4,5 and Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. 1 1

Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ x y , 0,2 . 2 2 Hence, y – 5 = 2 5 (x – 4) 0 4 3 y5 x 4 4 4 y5 3 x4 4y 20 3x12 3x 4y8 0 Thus, the required equation of the median through vertex R is 3x4y8 0. Question 10: Find the equation of the line passing through (-3, 5) and perpendicular to the line through the points (2, 5) and (-3, 6). Solution 10: 65 1 The slope of the line joining the points (2, 5) and (-3, 6) is m 3 2 5 We know that two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other. Therefore, slope of the line perpendicular to the line through the points (2, 5) and (-3, 6) 1 1 = 5 m 1 5 Now, the equation of the line passing through point (-3, 5), whose slope is 5, is y5 5( x3) y5 5x15 i. e.,5x y 20 0 Question **11**: A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ration 1: n. Find the equation of the line. Solution **11**: According to the section formula, the coordinates of the point that divides the line segment joining the points (1, 0) and (2, 3) in the ration 1: n is given by Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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