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NCERT solutions for Class 11 Mathematics chapter 10 - Straight Lines [Latest edition]

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Chapter 10: Straight Lines

Exercise 10.1Exercise 10.2Exercise 10.3Miscellaneous Exercise
Exercise 10.1 [Pages 211 - 212]

NCERT solutions for Class 11 Mathematics Chapter 10 Straight Lines Exercise 10.1 [Pages 211 - 212]

Exercise 10.1 | Q 1 | Page 211

Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.

Exercise 10.1 | Q 2 | Page 211

The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin. Find vertices of the triangle.

Exercise 10.1 | Q 3 | Page 211

Find the distance between P (x1, y1) and Q (x2, y2) when : (i) PQ is parallel to the y-axis, (ii) PQ is parallel to the x-axis

Exercise 10.1 | Q 4 | Page 211

Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).

Exercise 10.1 | Q 5 | Page 211

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, –4) and B (8, 0).

Exercise 10.1 | Q 6 | Page 212

Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.

Exercise 10.1 | Q 7 | Page 212

Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.

Exercise 10.1 | Q 8 | Page 212

Find the value of x for which the points (x, –1), (2, 1) and (4, 5) are collinear.

Exercise 10.1 | Q 9 | Page 212

Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.

Exercise 10.1 | Q 10 | Page 212

Find the angle between the x-axis and the line joining the points (3, –1) and (4, –2).

Exercise 10.1 | Q 11 | Page 212

The slope of a line is double of the slope of another line. If tangent of the angle between them is `1/3`, find the slopes of the lines

Exercise 10.1 | Q 12 | Page 212

A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k – y1 = m (h – x1).

Exercise 10.1 | Q 13 | Page 212

If three point (h, 0), (a, b) and (0, k) lie on a line, show that `q/h + b/k = 1`

Exercise 10.1 | Q 14 | Page 212

Consider the given population and year graph. Find the slope of the line AB and using it, find what will be the population in the year 2010?

Exercise 10.2 [Pages 219 - 220]

NCERT solutions for Class 11 Mathematics Chapter 10 Straight Lines Exercise 10.2 [Pages 219 - 220]

Exercise 10.2 | Q 1 | Page 219

Write the equations for the x and y-axes.

Exercise 10.2 | Q 2 | Page 219

Find the equation of the line which passes through the point (–4, 3) with slope `1/2`

Exercise 10.2 | Q 3 | Page 219

Find the equation of the line which passes though (0, 0) with slope m.

Exercise 10.2 | Q 4 | Page 219

Find the equation of the line which passes though `(2, 2sqrt3)` and is inclined with the x-axis at an angle of 75°

Exercise 10.2 | Q 5 | Page 219

Find the equation of the line which intersects the x-axis at a distance of 3 units to the left of origin with slope –2.

Exercise 10.2 | Q 6 | Page 219

Find the equation of the line which intersects the y-axis at a distance of 2 units above the origin and makes an angle of 30° with the positive direction of the x-axis.

Exercise 10.2 | Q 7 | Page 219

Find the equation of the line which passes through the points (–1, 1) and (2, –4).

Exercise 10.2 | Q 8 | Page 220

Find the equation of the line which is at a perpendicular distance of 5 units from the origin and the angle made by the perpendicular with the positive x-axis is 30°

Exercise 10.2 | Q 9 | Page 220

The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.

Exercise 10.2 | Q 10 | Page 220

Find the equation of the line passing through (–3, 5) and perpendicular to the line through the points (2, 5) and (–3, 6).

Exercise 10.2 | Q 11 | Page 220

A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio 1:n. Find the equation of the line.

Exercise 10.2 | Q 12 | Page 220

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).

Exercise 10.2 | Q 13 | Page 220

Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

Exercise 10.2 | Q 14 | Page 220

Find equation of the line through the point (0, 2) making an angle  `(2pi)/3` with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.

Exercise 10.2 | Q 15 | Page 220

The perpendicular from the origin to a line meets it at the point (– 2, 9), find the equation of the line.

Exercise 10.2 | Q 16 | Page 220

The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C

Exercise 10.2 | Q 17 | Page 220

The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre?

Exercise 10.2 | Q 18 | Page 220

P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is `x/a + y/b = 2`

 
Exercise 10.2 | Q 19 | Page 220

Point R (h, k) divides a line segment between the axes in the ratio 1:2. Find equation of the line.

Exercise 10.2 | Q 20 | Page 220

By using the concept of equation of a line, prove that the three points (3, 0), (–2, –2) and (8, 2) are collinear.

Exercise 10.3 [Pages 227 - 228]

NCERT solutions for Class 11 Mathematics Chapter 10 Straight Lines Exercise 10.3 [Pages 227 - 228]

Exercise 10.3 | Q 1.1 | Page 227

Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts.

x + 7y = 0

Exercise 10.3 | Q 1.2 | Page 227

Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts.

6x + 3y – 5 = 0

Exercise 10.3 | Q 1.3 | Page 227

Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts.

y = 0

Exercise 10.3 | Q 2.1 | Page 227

Reduce the following equation into intercept form and find their intercepts on the axes.

 3x + 2y – 12 = 0

Exercise 10.3 | Q 2.2 | Page 227

Reduce the following equation into intercept form and find their intercepts on the axes.

4x – 3y = 6

Exercise 10.3 | Q 2.3 | Page 227

Reduce the following equation into intercept form and find their intercepts on the axes.

3y + 2 = 0

Exercise 10.3 | Q 3.1 | Page 227

Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.

`x – sqrt3y + 8 = 0`

Exercise 10.3 | Q 3. (ii) | Page 227

Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.

y − 2 = 0

Exercise 10.3 | Q 3. (iii) | Page 227

Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.

x − y = 4

Exercise 10.3 | Q 4 | Page 227

Find the distance of the point (–1, 1) from the line 12(+ 6) = 5(– 2).

Exercise 10.3 | Q 5 | Page 227

Find the points on the x-axis, whose distances from the `x/3 +y/4 = 1`  are 4 units.

 
Exercise 10.3 | Q 6.1 | Page 227

Find the distance between parallel lines 15+ 8– 34 = 0 and 15+ 8+ 31 = 0

 

Exercise 10.3 | Q 6.2 | Page 227

Find the distance between parallel lines  (y) + = 0 and (y) – = 0

Exercise 10.3 | Q 7 | Page 228

Find equation of the line parallel to the line 3– 4y + 2 = 0 and passing through the point (–2, 3).

Exercise 10.3 | Q 8 | Page 228

Find equation of the line perpendicular to the line – 7+ 5 = 0 and having intercept 3.

Exercise 10.3 | Q 9 | Page 228

Find angles between the lines `sqrt3x + y = 1 and  x +     sqrt3y = 1`

Exercise 10.3 | Q 10 | Page 228

The line through the points (h, 3) and (4, 1) intersects the line 7x – 9y – 19 = 0at right angle. Find the value of h.

Exercise 10.3 | Q 11 | Page 228

Prove that the line through the point (x1y1) and parallel to the line Ax + By + C = 0 is A (x –x1B (y – y1) = 0.

Exercise 10.3 | Q 12 | Page 228

Two lines passing through the point (2, 3) intersects each other at an angle of 60°. If slope of one line is 2, find equation of the other line.

Exercise 10.3 | Q 13 | Page 228

Find the equation of the right bisector of the line segment joining the points (3, 4) and (1, 2).

Exercise 10.3 | Q 14 | Page 228

Find the coordinates of the foot of perpendicular from the point (1, 3) to the line 3– 4– 16 = 0.

Exercise 10.3 | Q 15 | Page 228

The perpendicular from the origin to the line y = mx + c meets it at the point (1, 2). Find the values of and c.

Exercise 10.3 | Q 16 | Page 228

If and are the lengths of perpendiculars from the origin to the lines cos θ – sin θ = cos 2θ and xsec θcosec θ = k, respectively, prove that p2 + 4q2 = k2

Exercise 10.3 | Q 17 | Page 228

In the triangle ABC with vertices A (2, 3), B (4, 1) and C (1, 2), find the equation and length of altitude from the vertex A.

Exercise 10.3 | Q 18 | Page 228

If is the length of perpendicular from the origin to the line whose intercepts on the axes are and b, then show that `1/p^2 = 1/a^2 + 1/b^2`

Miscellaneous Exercise [Pages 233 - 234]

NCERT solutions for Class 11 Mathematics Chapter 10 Straight Lines Miscellaneous Exercise [Pages 233 - 234]

Miscellaneous Exercise | Q 1 | Page 233

Find the values of k for which the line (k–3) x – (4 – k2) y + k2 –7k + 6 = 0 is 

(a) Parallel to the x-axis,

(b) Parallel to the y-axis,

(c) Passing through the origin.

Miscellaneous Exercise | Q 2 | Page 233

Find the values of q and p, if the equation x cos q + y sinq = p is the normal form of the line `sqrt3 x` + y + 2 = 0.

Miscellaneous Exercise | Q 3 | Page 233

Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and –6, respectively.

Miscellaneous Exercise | Q 4 | Page 233

What are the points on the y-axis whose distance from the line  `x/3 + y/4 = 1` is 4 units

Miscellaneous Exercise | Q 5 | Page 233

Find perpendicular distance from the origin to the line joining the points (cosΘ, sin Θ) and (cosΦ, sin Φ).

Miscellaneous Exercise | Q 6 | Page 233

Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines x– 7y + 5 = 0 and 3x + y = 0.

Miscellaneous Exercise | Q 7 | Page 233

Find the equation of a line drawn perpendicular to the line `x/4 + y/6 = 1`through the point, where it meets the y-axis.

Miscellaneous Exercise | Q 8 | Page 233

Find the area of the triangle formed by the lines y – x = 0, x + y = 0 and x – k = 0.

Miscellaneous Exercise | Q 9 | Page 233

Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.

Miscellaneous Exercise | Q 10 | Page 233

If three lines whose equations are y = m1x + c1, y = m2x + c2 and y = m3x + c3 are concurrent, then show that m1(c2 – c3) + m2 (c3 – c1) + m3 (c1 – c2) = 0.

Miscellaneous Exercise | Q 11 | Page 233

Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.

Miscellaneous Exercise | Q 12 | Page 233

Find the equation of the line passing through the point of intersection of the lines 4x + 7y – 3 = 0 and 2x– 3y + 1 = 0 that has equal intercepts on the axes.

Miscellaneous Exercise | Q 13 | Page 234

Show that the equation of the line passing through the origin and making an angle θ with the line `y = mx + c " is " y/c = (m+- tan theta)/(1 +- m tan theta)`

Miscellaneous Exercise | Q 14 | Page 234

In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?

Miscellaneous Exercise | Q 15 | Page 234

Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0.

Miscellaneous Exercise | Q 16 | Page 234

Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.

Miscellaneous Exercise | Q 17 | Page 234

The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (−4, 1). Find the equation of the legs (perpendicular sides) of the triangle.

Miscellaneous Exercise | Q 18 | Page 234

Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.

Miscellaneous Exercise | Q 19 | Page 234

If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.

Miscellaneous Exercise | Q 20 | Page 234

If sum of the perpendicular distances of a variable point P (x, y) from the lines x + y – 5 = 0 and 3x – 2y+ 7 = 0 is always 10. Show that P must move on a line.

Miscellaneous Exercise | Q 21 | Page 234

Find equation of the line which is equidistant from parallel lines 9+ 6y – 7 = 0 and 3x + 2y + 6 = 0.

Miscellaneous Exercise | Q 22 | Page 234

A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.

Miscellaneous Exercise | Q 23 | Page 234

Prove that the product of the lengths of the perpendiculars drawn from the points

`(sqrt(a^2 - b^2),0)` and `(-sqrta^2-b^2,0)` to the line `x/a cos theta + y/b sin theta = 1` is `b^2`

Miscellaneous Exercise | Q 24 | Page 234

A person standing at the junction (crossing) of two straight paths represented by the equations 2x – 3y+ 4 = 0 and 3x + 4y – 5 = 0 wants to reach the path whose equation is 6x – 7y + 8 = 0 in the least time. Find equation of the path that he should follow.

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Chapter 10: Straight Lines

Exercise 10.1Exercise 10.2Exercise 10.3Miscellaneous Exercise

NCERT solutions for Class 11 Mathematics chapter 10 - Straight Lines

NCERT solutions for Class 11 Mathematics chapter 10 (Straight Lines) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11 Mathematics 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 Class 11 solutions Straight Lines exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer NCERT Textbook Solutions to score more in exam.

Get the free view of chapter 10 Straight Lines Class 11 extra questions for Class 11 Mathematics and can use Shaalaa.com to keep it handy for your exam preparation

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