Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ Question 4: Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4). Solution 4: Let (a, 0) be the point on the X- axis that is equidistance from the points (7, 6) and (3, 4). 2 2 2 2 Accordingly, 7a 6 0 = 3a 4 0 2 2 49 a 14a 36 9 a 6a 16 2 2 a 14a 85 a 6a 25 On squaring both sides, we obtain 2 2 a 14a 85 a 6a 25 14a 6a 25 85 8a 60 60 15 a 8 2 15 Thus, the required point on the x-axis is ,0 2 Question 5: Find the slope of a line, which passes through the origin, and the mid-point of the segment joining the points P (0, -4) and B (8, 0). Solution 5: The coordinates of the mid-point of the line segment joining the points 08 4 0 P (0, -4) and B (8, 0) are , (4, 2) 2 2 It is known that the slope (m) of a non-vertical line passing through the points (x1, y1) and (x2, y2 y1 y2) is given by m , x2 x1 x x 2 1 Therefore, the slope of the line passing through (0, 0,) and (4, -2) is Hence, the required slope of the line is 1 . 2 2 0 2 1 40 4 2 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 6: Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (-1, -1) are vertices of a right angled triangle. Solution 6: The vertices of the given triangle are A (4, 4), B (3, 5), and C (-1, -1). It is known that the slope (m) of a non-vertical line passing through the points (x1, y1) and (x2, y2 y1 y2) is given by m , x2 x1 x2 x1 54 Slope of AB m1 1 34 1 5 6 3 Slope of BC m2 1 3 4 2 41 5 Slope of CA m3 1 41 5 It is observed that mm 1 3= -1 This shows that line segments AB and CA are perpendicular to each other i.e., the given triangle is right-angled at A (4, 4). 4,4 , 3,5 , and 1, 1 are the vertices of a right-angled triangle. Thus, the points Question 7: Find the slope of the line, which makes an angle of 30 with the positive direction of y-axis measured anticlockwise. Solution 7: If a line makes an angle of 30 with positive direction of the y-axis measured anticlockwise, then the angle made by the line with the positive direction of the x-axis measured anticlockwise is 90 30 120 . Thus, the slope of the given line is tan 120 = tan 180 60 tan 60 3 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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