Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ 1 2 4 12 5 2 unit 2 1 2 48 10 unit 2 2 1 58 unit 2 2 1 58unit 2 2 29unit Area of ACD 1 2 = 45 25( 2 5) 45 5 unit 2 1 4 2 3 5( 7) 4 10 unit 2 1 12 35 40 unit 2 2 1 63 unit 2 2 63 unit 2 2 63 58 63 121 Thus, area (ABCD) = 29 unit unit unit 2 2 2 2 2 2 Question 2: The base of an equilateral triangle with side 2a lies along the y-axis such that the midpoint of the base is at the origin. Find vertices of the triangle. Solution 2: Let ABC be the given equilateral triangle with side 2a. Accordingly, AB = BC = CA = 2a Assume that base BC lies along the y-axis such that the mid-point of BC is at the origin. i.e., BO = OC = a, where O is the origin. Now, it is clear that the coordinates of point C are (0, a), while the coordinates of point B are (0, -a). It is known that the line joining a vertex of an equilateral triangle with the mid-point of its opposite side is perpendicular. Hence, vertex A lies on the y-axis. 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 ______________________________________________________________________________ On applying Pythagoras theorem to AOC, we obtain 2 2 2 2 2a OA a 2 2 2 4a a OA 2 2 OA 3a 2 2 (AC) OA OC OA= 3a Coordinates of point A = 3 a,0 a and a or a a and a Thus, the vertices of the given equilateral triangle are 0,a , 0, , 3 ,0 (0, ), 0, , 3 ,0 Question 3: Find the distance between Px , and Qx , PQ is parallel to the x-axis. Solution 3: y y when : (i) PQ is parallel to the y-axis, (ii) 1 1 2 2 The given points are Px , and Qx , y y . 1 1 2 2 (i) When PQ is parallel to the y-axis, x1 = x2. 2 2 2 1 2 1 In this case, distance between P and Q = x x y y y y 2 y 2 1 y 2 1 2 2 2 1 2 1 (ii) In this case, distance between P and Q = x x y y x x 2 2 1 x x 2 1 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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