Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ On solving equation (1) and (2), we obtain 2m 5m2 x and y m1 m1 2m 5m2 , m1 m1 is the point of intersection of line (1) and (2). Since this point is at a distance of 3 units from points (-1, 2), accordingly to distance formula, m1 m1 2 2 2m 5m2 1 2 3 m1 m1 2 2 2 2 2 2m m1 5m 22m 2 3 m 1 m 1 2 9 9m 9 2 1 m m1 1 2 2 2 1 m m 1 2m 2m 0 m 0 Thus, the slope of the required line must be zero i.e., the line must be parallel to the x-axis. Question 18: Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror. Solution 18: The equation of the given line is x + 3y = 7 …(1) Let point B (a, b) be the image of point A (3, 8). Accordingly, line (1) is the perpendicular bisector of AB. 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 ______________________________________________________________________________ b8 Slope of AB = a 3 , while the slope of the line (1) = 1 3 Since line (1) is perpendicular to AB, b8 1 1 a3 3 b8 1 3a 9 b8 3a 9 3a b1 ... 2 a3 b8 Mid-Point of AB = , 2 2 The mid-point of the line segment AB will also satisfy line (1). Hence, from equation (1), we have a3 b8 3 7 2 2 a33b 24 14 a3b 13 ... 3 On solving equations (2) and (3), we obtain a = -1 and b = -4. Thus, the image of the given point with respect to the given line is (-1, -4). Question 19: If the lines y = 3x + 1 and 2y = x + 3 are equally indicated to the line y = mx + 4, find the value of m. Solution 19: The equation of the given lines are y = 3x + 1 …(1) 2y = x + 3 …(2) y = mx + 4 …(3) Slope of line (1), m 1 = 3 1 Slope of line (2), m2 2 Slope of line (3), m 3 = m It is given that lines (1) and (2) are equally inclined to line (3). This means that the given angle between lines (1) and (3) equals the angle between lines (2) and (3). m1 m3 m2 m3 1m m 1m m 1 3 2 3 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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