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

#### Chapters ## Chapter 10: Straight Lines

[Pages 211 - 212]

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

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.

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.

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

Q 4 | Page 211

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

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.

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.

Q 8 | Page 212

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

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.

Q 10 | Page 212

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

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

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).

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

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? [Pages 219 - 220]

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

Q 1 | Page 219

Write the equations for the x and y-axes.

Q 2 | Page 219

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

Q 3 | Page 219

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

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°

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.

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.

Q 7 | Page 219

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

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°

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.

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.

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).

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.

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).

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.

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.

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.

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

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?

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

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.

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.

[Pages 227 - 228]

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

Q 1 | Page 227

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

(i) + 7= 0

(ii) 6+ 3– 5 = 0

(iii) = 0

Q 2 | Page 227

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

(i) 3+ 2– 12 = 0

(ii) 4– 3= 6

(iii) 3+ 2 = 0

Q 3 | Page 227

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

i) x – sqrt3y + 8 = 0

(ii) – 2 = 0

(iii) – = 4

Q 4 | Page 227

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

Q 5 | Page 227

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

Q 6.1 | Page 227

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

Q 6.2 | Page 227

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

Q 7 | Page 228

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

Q 8 | Page 228

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

Q 9 | Page 228

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

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.

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.

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.

Q 13 | Page 228

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

Q 14 | Page 228

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

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.

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

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.

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

[Pages 233 - 234]

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

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.

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.

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.

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

Q 5 | Page 233

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

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.

Q 7 | Page 233

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

Q 8 | Page 233

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

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.

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.

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.

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.

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)

Q 14 | Page 234

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

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.

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.

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.

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.

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.

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.

Q 21 | Page 234

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

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.

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

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.

[Page 211]

### NCERT solutions for Class 11 Mathematics Textbook Chapter 10 Straight Lines [Page 211]

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).

## Chapter 10: Straight Lines ## NCERT solutions for Class 11 Mathematics Textbook chapter 10 - Straight Lines

NCERT solutions for Class 11 Mathematics Textbook 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 Textbook solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 11 Mathematics Textbook chapter 10 Straight Lines are Slope of a Line, Various Forms of the Equation of a Line, General Equation of a Line, Distance of a Point from 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.

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