Maharashtra State Board 11th Maths Solutions Chapter 5 Straight Line Ex 5.2
Question 1
Maharashtra Board Solution
Find the slope of each of the lines which passes through the following points: i. A(2, -1), B(4,3) ii. C(- 2,3), D(5, 7) iii. E(2,3), F(2, – 1) iv. G(7,1), H(- 3,1)
Solution & Step-by-Step Answer:
i. Here, A = (2, -1) andB = (4, 3) Slope of line AB = = 2
ii. Here, C = (-2, 3) and D = (5, 7)
Slope of line CD =
iii. Here, E s (2, 3) and F = (2, -1)
Slope of line EF = , which ix not defined.
Alternate Method:
Points E and F have same x co-ordinates i.e. 2.
Points E and F lie on a line parallel to Y-axis.
∴ The slope of EF is not defined.
iv. Here, G = (7, 1) and H = (-3, 1)
Slope of line GH = = o
Alternate Method:
Points G and H have same y co-ordinate i.e. 1.
∴ Points G and H lie on a line parallel to the
X-axis.
∴ The slope of GH is 0.
Question 2
Maharashtra Board Solution
If the x and x-intercepts of line L are 2 and 3 respectively, then find the slope of line L.
Solution & Step-by-Step Answer:
Given, x-intercept of line L is 2 and y-intercept of line L is 3 ∴ The line L intersects X-axis at (2, 0) and Y-axis at (0,3). ∴ The line L passes through (2, 0) and (0, 3). Slope of line L =
Question 3
Maharashtra Board Solution
Find the slope of the line whose inclination is 30°.
Solution & Step-by-Step Answer:
Given, inclination (θ) = 30° ∴ Slope of the line = tanθ = tan30° =
Question 4
Maharashtra Board Solution
Find the slope of the line whose inclination is
Solution & Step-by-Step Answer:
Given, inclination (0) = ∴ Slope of the line = tan θ = tan = 1
Question 5
Maharashtra Board Solution
A line makes intercepts 3 and 3 on the co-ordinate axes. Find the inclination of the line.
Solution & Step-by-Step Answer:
Given, x-intercept of line is 3 and y-intercept of line is 3 ∴ The line intersects X-axis at (3, 0) and Y-axis at (0, 3). ∴ The line passes through (3, 0) and (0,3). ∴ Slope of line = = -1 But, slope of a line = tan θ ∴ tan θ = – 1 = – tan = tan(π- ) …[v tan(π – θ) = -tan θ] tan θ = tan θ = The inclination of the line is . [Note: Answer given in the textbook is ‘-1 However, as per our calculation it is ]
Question 6
Maharashtra Board Solution
Without using Pythagoras theorem, show that points A (4, 4), B (3, 5) and C (- 1, – 1) are the vertices of a right-angled triangle.
Solution & Step-by-Step Answer:
Given, A(4,4), B(3, 5), C (-1, -1). Slope of AB = = – 1 Slope of BC = Slope of AC = = 1 Slope of AB x slope of AC = – 1 x 1 = – 1 ∴ side AB ⊥ side AC ∴ ∆ABC is a right angled triangle right angled at A. ∴ The given points are the vertices of a right angled triangle.
Question 7
Maharashtra Board Solution
Find the slope of the line which makes angle of 45° with the positive direction of the Y-axis measured anticlockwise.
Solution & Step-by-Step Answer:
Since the line makes an angle of 45° with positive direction of Y-axis in anticlockwise direction, Inclination of the line (0) = (90° + 45°) ∴ Slope of the line = tan(90° + 45°) = – cot 45° = -1
Question 8
Maharashtra Board Solution
Find the value of k for which the points P(k, -1), Q(2,1) and R(4,5) are collinear.
Solution & Step-by-Step Answer:
Given, points P(k, – 1), Q (2, 1) and R(4, 5) are collinear. ∴ Slope of PQ = Slope of QR. ∴ ∴ ∴ 4 = 4 (2 – k) ∴ 1 = 2 – k ∴ k = 2 – 1 = 1
Question 9
Maharashtra Board Solution
Find the acute angle between the X-axis and the line joining the points A(3, -1) and B(4, – 2).
Solution & Step-by-Step Answer:
Given, A (3, – 1) and B (4, – 2) Slope of AB = = – 1 But, slope of a line = tan θ ∴ tan θ = – 1 = – tan 45° = tan (180° -45°) … [∵ tan (180° – θ) = -tan θ] = tan 135° ∴ θ = 135° Let α be the acute angle that line AB makes with X-axis. Then, α + 0 = 180° α = 180°- 135° = 45° ∴ The acute angle between the X-axis and the line joining the points A and B is 45°.
Question 10
Maharashtra Board Solution
A line passes through points A(xi, y0 and B(h, k). If the slope of the line is m, then show that k – y1 = m (h – x1).
Solution & Step-by-Step Answer:
Given, A(x1, y1), B(h, k) and slope of line AB = m Slope of line AB = ∴ m = ∴ k – y1 = m (h – x1)
Question 11
Maharashtra Board Solution
If the points A(h, 0), B(0, k) and C(a, b) lie on a line, then show that = 1. ‘
Solution & Step-by-Step Answer:
Given, A(h, 0), B(0, k) and C(a, b) Since the points A, B and C lie on a line, they are collinear. ∴ Slope of AB = slope of BC
