Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ n 1 1 2 0 1 3 2 3 , n n , 1 n 1 n n 1 n 1 The slope of the line joining the points (1, 0) and (2, 3) is 30 m 3 21 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 that is perpendicular to the line joining the points (1, 0) and (2, 3) = 1 1 m 3 Now the equation of the line passing through 3 1 n 2 y x n1 3 n1 3 n 1 y 3 xn 1 n 2 3n 1 y 9 n 1 x n 2 1 n x 31 n y n **11** n2 3 , n1 n1 and whose slope is 1 is given by 3 Question 12: Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the points (2, 3). Solution 12: The equation of a line in the intercept form is x y 1 ….(i) a b Here, a and b are the intercepts on x and y axes respectively. It is given that the line cuts off equal intercepts on both the axes. This means that a = b. Accordingly, equation (i) reduces to x y 1 a a x y a ... ii Since the given line passes through point (2, 3), equation (ii) reduces to 2 + 3 = a a = 5 On substituting the value of a in equation (ii), we obtain x + y = 5, which is the required equation of the line. 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 ______________________________________________________________________________ Question 13: Find the equation of the line passing through the points (2, 2) and cutting off intercepts on the axes whose sum is 9. Solution 13: The equation of a line in the intercept form is x y 1 …(i) a b Here, a and b are the intercepts on x and y axes respectively. It is given that a + b = 9 b = 9 – a …(ii) From equation (i) and (ii), we obtain x y 1 …(iii) a 9a It is given that the line passes through point (2, 2). Therefore, equation (iii) reduces to 2 2 1 a 9a 1 1 2 1 a 9 a 9aa 2 1 a9 a 18 1 2 9a a 2 18 9a a 2 a a 9 18 0 2 a a a 6 3 18 0 a a a a a ( 6) 3 6 0 6 3 0 a 6 or a = 3 If a = 6 and b = 9 – 6 = 3, then the equation of the line is x y 1 x2y6 0 6 3 If a = 3 and b = 9 – 3 = 6, then the equation of the line is x y 12x y6 0 3 6 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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Class XI Chapter 12 - Introduction

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