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Chapters
2: Relations and Functions
3: Trigonometric Functions
4: Principle of Mathematical Induction
5: Complex Numbers and Quadratic Equations
6: Linear Inequalities
7: Permutations and Combinations
8: Binomial Theorem
9: Sequences and Series
▶ 10: Straight Lines
11: Conic Sections
12: Introduction to Three Dimensional Geometry
13: Limits and Derivatives
14: Mathematical Reasoning
15: Statistics
16: Probability
![NCERT Exemplar solutions for Mathematics [English] Class 11 chapter 10 - Straight Lines - Shaalaa.com](/images/mathematics-english-class-11_6:5f2b1b2038084cf381bfa42c826a928c.jpg "NCERT Exemplar solutions for Mathematics [English] Class 11 chapter 10 - Straight Lines")
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Solutions for Chapter 10: Straight Lines
Below listed, you can find solutions for Chapter 10 of CBSE NCERT Exemplar for Mathematics [English] Class 11.
NCERT Exemplar solutions for Mathematics [English] Class 11 10 Straight Lines Solved Examples [Pages 168 - 177]
Short Answer
Find the equation of a line which passes through the point (2, 3) and makes an angle of 30° with the positive direction of x-axis.
Find the equation of the line where length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of x-axis is 30°.
Prove that every straight line has an equation of the form Ax + By + C = 0, where A, B and C are constants.
Find the equation of the straight line passing through (1, 2) and perpendicular to the line x + y + 7 = 0.
Find the distance between the lines 3x + 4y = 9 and 6x + 8y = 15.
Show that the locus of the mid-point of the distance between the axes of the variable line x cosα + y sinα = p is `1/x^2 + 1/y^2 = 4/p^2` where p is a constant.
If the line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlock wise direction through an angle of 15°. Find the equation of the line in new position.
Long Answer
If the slope of a line passing through the point A(3, 2) is `3/4`, then find points on the line which are 5 units away from the point A.
Find the equation to the straight line passing through the point of intersection of the lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x – 5y + 11 = 0.
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). Find the coordinates of the point A.
If one diagonal of a square is along the line 8x – 15y = 0 and one of its vertex is at (1, 2), then find the equation of sides of the square passing through this vertex.
Objective Type Questions 12 to 30
The inclination of the line x – y + 3 = 0 with the positive direction of x-axis is ______.
45°
135°
– 45°
–135°
The two lines ax + by = c and a′x + b′y = c′ are perpendicular if ______.
aa′ + bb′ = 0
ab′ = ba′
ab + a′b′ = 0
ab′ + ba′ = 0
The equation of the line passing through (1, 2) and perpendicular to x + y + 7 = 0 is ______.
y – x + 1 = 0
y – x – 1 = 0
y – x + 2 = 0
y – x – 2 = 0.
The distance of the point P(1, – 3) from the line 2y – 3x = 4 is ______.
13
`7/13 sqrt(13)`
`sqrt(13)`
None of these
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 are ______.
(–6, 5)
(5, 6)
(–5, 6)
(6, 5)
The intercept cut off by a line from y-axis is twice than that from x-axis, and the line passes through the point (1, 2). The equation of the line is ______.
2x + y = 4
2x + y + 4 = 0
2x – y = 4
2x – y + 4 = 0
A line passes through P(1, 2) such that its intercept between the axes is bisected at P. The equation of the line is ______.
x + 2y = 5
x – y + 1 = 0
x + y – 3 = 0
2x + y – 4 = 0
The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is ______.
(– 1, – 14)
(3, 4)
(0, 0)
(1, 2)
A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. The locus of the point is ______.
3x2 + 4y2 = 192
4x2 + 3y2 = 192
x2 + y2 = 192
None of these
NCERT Exemplar solutions for Mathematics [English] Class 11 10 Straight Lines Exercise [Pages 178 - 185]
Short Answer
Find the equation of the straight line which passes through the point (1, – 2) and cuts off equal intercepts from axes.
Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, – 1).
Find the angle between the lines y = `(2 - sqrt(3)) (x + 5)` and y = `(2 + sqrt(3))(x - 7)`
Find the equation of the lines which passes through the point (3, 4) and cuts off intercepts from the coordinate axes such that their sum is 14.
Find the points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10.
Show that the tangent of an angle between the lines `x/a + y/b` = 1 and `x/a - y/b` = 1 is `(2ab)/(a^2 - b^2)`
Find the equation of lines passing through (1, 2) and making angle 30° with y-axis.
Find the equation of the line passing through the point of intersection of 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.
For what values of a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x – 3y + 6 = 0 on the axes.
If the intercept of a line between the coordinate axes is divided by the point (–5, 4) in the ratio 1 : 2, then find the equation of the line.
Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of x-axis.
Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2).
Long Answer
If the equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, – 1), then find the length of the side of the triangle.
A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P.
In what direction should a line be drawn through the point (1, 2) so that its point of intersection with the line x + y = 4 is at a distance `sqrt(6)/3` from the given point.
A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.
Find the equation of the line which passes through the point (– 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point.
Find the equations of the lines through the point of intersection of the lines x – y + 1 = 0 and 2x – 3y + 5 = 0 and whose distance from the point (3, 2) is `7/5`
If the sum of the distances of a moving point in a plane from the axes is 1, then find the locus of the point.
P1, P2 are points on either of the two lines `- sqrt(3) |x|` = 2 at a distance of 5 units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from P1, P2 on the bisector of the angle between the given lines.
If p is the length of perpendicular from the origin on the line `x/a + y/b` = 1 and a2, p2, b2 are in A.P, then show that a4 + b4 = 0.
Objective Type Questions from 22 to 41
A line cutting off intercept – 3 from the y-axis and the tangent at angle to the x-axis is `3/5`, its equation is ______.
5y – 3x + 15 = 0
3y – 5x + 15 = 0
5y – 3x – 15 = 0
None of these
Slope of a line which cuts off intercepts of equal lengths on the axes is ______.
– 1
– 0
2
`sqrt(3)`
The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.
x – y = 5
x + y = 5
x + y = 1
x – y = 1
The equation of the line passing through the point (1, 2) and perpendicular to the line x + y + 1 = 0 is ______.
y – x + 1 = 0
y – x – 1 = 0
y – x + 2 = 0
y – x – 2 = 0
The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is ______.
`(a^2 - b^2)/(ab)`
`(b^2 - a^2)/2`
`(b^2 - a^2)/(2ab)`
None of these
If the line `x/"a" + y/"b"` = 1 passes through the points (2, –3) and (4, –5), then (a, b) is ______.
(1, 1)
(– 1, 1)
(1, – 1)
(– 1, –1)
The distance of the point of intersection of the lines 2x – 3y + 5 = 0 and 3x + 4y = 0 from the line 5x – 2y = 0 is ______.
`130/(17sqrt(29))`
`13/(7sqrt(29))`
`130/7`
None of these
The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line `sqrt(3) x + y` = 1 is ______.
y + 2 = 0, `sqrt(3) x - y - 2 - 3 sqrt(3)` = 0
x – 2 = 0, `sqrt(3)x - y + 2 + 3 sqrt(3)` = 0
`sqrt(3) x - y - 2 - 3sqrt(3)` = 0
None of these
The equations of the lines passing through the point (1, 0) and at a distance `sqrt(3)/2` from the origin, are ______.
`sqrt(3)x + y - sqrt(3)` = 0, `sqrt(3)x - y - sqrt(3)` = 0
`sqrt(3)x + y + sqrt(3)` = 0, `sqrt(3)x - y + sqrt(3)` = 0
`x + sqrt(3)y - sqrt(3)` = 0, `x - sqrt(3)y - sqrt(3)` = 0
None of these
The distance between the lines y = mx + c1 and y = mx + c2 is ______.
`(c_1 - c_2)/sqrt(m^2 + 1)`
`|c_1 - c_2|/sqrt(1 + m^2)`
`(c_2 - c_1)/sqrt(1 + m^2)`
0
The coordinates of the foot of perpendiculars from the point (2, 3) on the line y = 3x + 4 is given by ______.
`37/10, (-1)/10`
`(-1)/10, 37/10`
`10/37, -10`
`2/3, -1/3`
If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be ______.
2x + 3y = 12
3x + 2y = 12
4x – 3y = 6
5x – 2y = 10
Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is ______.
y + 2 = x + 1
y + 2 = 3 (x + 1)
y – 2 = 3 (x – 1)
y – 2 = x – 1
Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are ______.
y = x, y + x = 1
y = x, x + y = 2
2y = x, y + x = `1/3`
y = 2x, y + 2x = 1
For specifying a straight line, how many geometrical parameters should be known?
1
2
4
3
The point (4, 1) undergoes the following two successive transformations:
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are ______.
(4, 3)
(3, 4)
(1, 4)
`7/2, 7/2`
A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 is ______.
(1, –1)
(1, 1)
(0, 0)
(0, 1)
A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is ______.
`1/3`
`2/3`
1
`4/3`
The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the lines 3x + 4y + 5 = 0 and 3x + 4y – 5 = 0 is ______.
1 : 2
3 : 7
2 : 3
2 : 5
One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is ______.
(–1, –1)
(2, 2)
(–2, –2)
(2, –2)
Fill in the blank 42 to 47
If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through ______.
The line which cuts off equal intercept from the axes and pass through the point (1, –2) is ______.
Equations of the lines through the point (3, 2) and making an angle of 45° with the line x – 2y = 3 are ______.
The points (3, 4) and (2, – 6) are situated on the ______ of the line 3x – 4y – 8 = 0.
A point moves so that square of its distance from the point (3, –2) is numerically equal to its distance from the line 5x – 12y = 3. The equation of its locus is ______.
Locus of the mid-points of the portion of the line x sin θ + y cos θ = p intercepted between the axes is ______.
State whether the following is True or False: 48 to 56
If the vertices of a triangle have integral coordinates, then the triangle can not be equilateral.
True
False
The points A(– 2, 1), B(0, 5), C(– 1, 2) are collinear.
True
False
Equation of the line passing through the point (a cos3θ, a sin3θ) and perpendicular to the line x sec θ + y cosec θ = a is x cos θ – y sin θ = a sin 2θ.
True
False
The straight line 5x + 4y = 0 passes through the point of intersection of the straight lines x + 2y – 10 = 0 and 2x + y + 5 = 0.
True
False
The vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is x + y = 2. Then the other two sides are y – 3 = `(2 +- sqrt(3)) (x - 2)`.
True
False
The equation of the line joining the point (3, 5) to the point of intersection of the lines 4x + y – 1 = 0 and 7x – 3y – 35 = 0 is equidistant from the points (0, 0) and (8, 34).
True
False
The line `x/a + y/b` = 1 moves in such a way that `1/a^2 + 1/b^2 = 1/c^2`, where c is a constant. The locus of the foot of the perpendicular from the origin on the given line is x2 + y2 = c2.
True
False
The lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent if a, b, c are in G.P.
True
False
Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).
True
False
Match the column C1 and C2: 57 to 59
| Column C1 | Column C2 |
| (a) The coordinates of the points P and Q on the line x + 5y = 13 which are at a distance of 2 units from the line 12x – 5y + 26 = 0 are |
(i) (3, 1), (–7, 11) |
| (b) The coordinates of the point on the line x + y = 4, which are at a unit distance from the line 4x + 3y – 10 = 0 are |
(ii) `(- 1/3, 11/3), (4/3, 7/3)` |
| (c) The coordinates of the point on the line joining A (–2, 5) and B (3, 1) such that AP = PQ = QB are |
(iii) `(1, 12/5), (-3, 16/5)` |
The value of the λ, if the lines (2x + 3y + 4) + λ (6x – y + 12) = 0 are
| Column C1 | Column C2 |
| (a) Parallel to y-axis is | (i) λ = `-3/4` |
| (b) Perpendicular to 7x + y – 4 = 0 is | (ii) λ = `-1/3` |
| (c) Passes through (1, 2) is | (iii) λ = `-17/41` |
| (d) Parallel to x axis is | λ = 3 |
The equation of the line through the intersection of the lines 2x – 3y = 0 and 4x – 5y = 2 and
| Column C1 | Column C2 |
| (a) Through the point (2, 1) is | (i) 2x – y = 4 |
| (b) Perpendicular to the line (ii) x + y – 5 = 0 x + 2y + 1 = 0 is |
(ii) x + y – 5 = 0 |
| (c) Parallel to the line (iii) x – y –1 = 0 3x – 4y + 5 = 0 is |
(iii) x – y –1 = 0 |
| (d) Equally inclined to the axes is | (iv) 3x – 4y – 1 = 0 |
Solutions for 10: Straight Lines
NCERT Exemplar solutions for Mathematics [English] Class 11 chapter 10 - Straight Lines
Shaalaa.com has the CBSE Mathematics Mathematics [English] Class 11 CBSE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT Exemplar solutions for Mathematics Mathematics [English] Class 11 CBSE 10 (Straight Lines) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. NCERT Exemplar textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.
Concepts covered in Mathematics [English] Class 11 chapter 10 Straight Lines are Slope of a Line, Various Forms of the Equation of a Line, General Equation of a Line, Brief Recall of Two Dimensional Geometry from Earlier Classes, Shifting of Origin, Equation of Family of Lines Passing Through the Point of Intersection of Two Lines, Distance of a Point from a Line.
Using NCERT Exemplar Mathematics [English] Class 11 solutions Straight Lines exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in NCERT Exemplar Solutions are essential questions that can be asked in the final exam. Maximum CBSE Mathematics [English] Class 11 students prefer NCERT Exemplar Textbook Solutions to score more in exams.
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