Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ Question 8: Find the value of X for which the points (x, -1), (2, 1) and (4, 5) are collinear. Solution 8: If points A (x, -1), B (2, 1), and C (4, 5) are collinear, then Slope of AB = Slope of BC 1 1 51 2x 42 **11** 4 2 x 2 2 2 2 x 2 42x 2x 2 x 1 Thus, the required value of x is 1. Question 9: Without using distance formula, show that points 2, 1 , 4,0 , 3,3 and 3,2 of a parallelogram. are vertices Solution 9: 2, 1 , 4,0 , 3,3 and 3,2 be respectively denoted by A, B, C, and D. Let points 0+1 1 Slopes of AB = 4+2 6 2-3 1 1 Slopes of CD = -3-3 6 6 Slope of AB = Slope of CD AB and CD are parallel to each other. 3-0 3 Now, slope of BC = 3 3-4 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 ______________________________________________________________________________ 2+1 3 Slope of AD = 3 -3+2 1 Slope of BC = Slope of AD BC and AD are parallel to each other. Therefore, both pairs of opposite side of quadrilateral ABCD are parallel. Hence, ABCD is a parallelogram. Thus, points 2, 1 , 4,0 , 3,3 and 3,2 are the vertices of a parallelogram. Question 10: Find the angle between the x-axis and the line joining the points (3, -1) and (4, -2). Solution 10: 2 1 The slope of the line joining the points (3, -1) and (4, -2) is m 2 1 1 43 Now, the inclination ( ) of the line joining the points (3, -1) and (4, -2) is given by tan = -1 90 45 135 Thus, the angle between the x-axis and the line joining the points (3, -1) and (4, -2) is 135 Question **11**: The slope of a line is double of the slope of another line. If tangent of the angle between them is 1 , find the slope of the lines. 3 Solution **11**: Let m1, m be the slopes of the two given lines such that m1 = 2m. l and l with slopes m and m then We know that if is the angle between the lines 1 2 1 2 m m tan 1 m m 2 1 1 2 It is given that the tangent of the angle between the two lines is 1 3 . 1 m2m 3 1 2 m . m 1 m 2 3 1 2m 1 m 1 m m or 2 2 2 3 1 2m 3 1 2m 1 2m Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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