# 10. Straight Lines

##### 19 LECTURES

• This page has links to complete syllabus of NCERT Chapter 10 Straight Lines based on syllabus recommended by CBSE based on class 11 maths.
• There are 19 video lectures having explanations from basic to advance concepts, each and every NCERT solutions, questions and all important examples. You can access them directly from the lecture menu or just scroll down the page.
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##### 10(A) || How I am going to teach you Straight Lines? Meaning of Equation!

00:00:03 How to study Straight Lines (Coordinate Geometry)

00:08:51 Arrangement of Straight Lines topic in NCERT

00:09:45 Meaning and Definition of Equation through Animations

00:18:51 How to find equation of any mathematical shape? Equation of Circle through Definition of Circle

##### 10(B) || Meaning and Purpose of Slope of a Line!

00:00:05 Logical and Algebraical Meaning of Slope of a Line

00:09:45 We can find slope of line using any two passing points of line with proof

00:16:15 Relationship of Slope of line with angle made with positive direction of x-axis measured counter clockwise

00:23:55 How to judge graphical representation of a line using slope

##### 10(C) || Exercise 10.1 Angle between two lines

00:00:05 Derivation for angles between two lines using their slopes

00:18:25 Condition of slopes if two lines are parallel

00:20:15 Condition of slopes if two lines are perpendicular

00:23:55 NCERT Exercise 10.1 Question 1 Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.

00:31:05 NCERT Exercise 10.1 Question 2 The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

00:40:35 NCERT Exercise 10.1 Question 3 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.

00:45:25 NCERT Exercise 10.1 Question 4 Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).

00:48:05 NCERT Exercise 10.1 Question 5 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).

00:54:35 NCERT Exercise 10.1 Question 6 Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.

01:01:15 NCERT Exercise 10.1 Question 7 Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.

##### 10(D) || Exercise 10.1

00:00:20 NCERT Exercise 10.1 Question 8 Find the value of x for which the points (x, – 1), (2,1) and (4, 5) are collinear.

00:05:23 NCERT Exercise 10.1 Question 9 Without using distance formula, show that points (– 2, – 1), (4, 0), (3, 3) and (–3, 2) are the vertices of a parallelogram.

00:09:43 NCERT Exercise 10.1 Question 10 Find the angle between the x-axis and the line joining the points (3,–1) and (4,–2).

00:15:03 NCERT Exercise 10.1 Question 12 A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k – y1 = m (h – x1 ).

00:16:13 NCERT Exercise 10.1 Question 13 If three points (h, 0), (a, b) and (0, k) lie on a line, show that a/h + b/k =1

00:20:03 NCERT Exercise 10.1 Question 14 Consider the following population and year graph (Fig 10.10), find the slope of the line AB and using it, find what will be the population in the year 2010?

00:25:23 NCERT Exercise 10.1 Question 11 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.

00:33:45 Equation of line using area of triangle rule and collinear condition

##### 10(E) || Exercise 10.2 (Q1 to Q8)

00:00:04 Minimum information required to form any equation

00:02:53 Point Slope form of Equation of a straight line

In Exercises 1 to 8, find the equation of the line which satisfy the given conditions:

00:09:44 NCERT Exercise 10.2 Question 2 Passing through the point (– 4, 3) with slope 1/2.

00:14:04 NCERT Exercise 10.2 Question 3 Passing through (0, 0) with slope m.

00:16:14 NCERT Exercise 10.2 Question 1 (Equation of x-axis and y-axis) Write the equations for the x-and y-axes.

00:25:34 NCERT Exercise 10.2 Question 4 Passing through (2,2 sqrt 3) and inclined with the x-axis at an angle of 750.

00:32:43 NCERT Exercise 10.2 Question 5 Intersecting the x-axis at a distance of 3 units to the left of origin with slope –2.

00:35:33 NCERT Exercise 10.2 Question 6 Intersecting the y-axis at a distance of 2 units above the origin and making an angle of 300 with positive direction of the x-axis.

00:38:43 NCERT Exercise 10.2 Question 7 Passing through the points (–1, 1) and (2, – 4).

00:43:13 NCERT Exercise 10.2 Question 8 Perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 300.

##### 10(F) || Derivations of All Rules

DERIVATIONS OF FORMULAS TO FIND EQUATION OF STRAIGHT LINES

00:03:15 Two-point form

00:06:15 NCERT Exercise 10.2 Question 7 using Two point form Passing through the points (–1, 1) and (2, – 4).

00:07:25 Slope intercept form and meaning of intercept

00:12:15 NCERT Exercise 10.2 Question 5 using Slope intercept form Intersecting the x-axis at a distance of 3 units to the left of origin with slope –2.

00:15:35 NCERT Exercise 10.2 Question 6 using Slope intercept form Intersecting the y-axis at a distance of 2 units above the origin and making an angle of 300 with positive direction of the x-axis. 00:18:35 Intercept form

00:25:25 Normal Form of Straight Line

00:34:25 NCERT Exercise 10.2 Question 8 using Normal Form Perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 300.

##### 10(G) || Exercise 10.2 (Q9 to Q13)

00:01:16 NCERT Exercise 10.2 Question 9 The vertices of ∆ PQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.

00:09:56 NCERT Exercise 10.2 Question 10 Find the equation of the line passing through (–3, 5) and perpendicular to the line through the points (2, 5) and (–3, 6).

00:17:46 NCERT Exercise 10.2 Question 11 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.

00:28:06 NCERT Exercise 10.2 Question 12 Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).

00:35:16 NCERT Exercise 10.2 Question 13 Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

##### 10(H) || Exercise 10.2 (Q14 to Q20)

00:00:35 NCERT Exercise 10.2 Question 14 Find equation of the line through the point (0, 2) making an angle 2π/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.

00:05:35 NCERT Exercise 10.2 Question 15 The perpendicular from the origin to a line meets it at the point (–2, 9), find the equation of the line.

00:11:05 NCERT Exercise 10.2 Question 16 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.

00:18:55 NCERT Exercise 10.2 Question 17 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?

00:22:55 NCERT Exercise 10.2 Question 18 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.

00:27:35 NCERT Exercise 10.2 Question 19 Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find equation of the line.

00:36:45 NCERT Exercise 10.2 Question 20 By using the concept of equation of a line, prove that the three points (3, 0), (– 2, – 2) and (8, 2) are collinear.

##### 10(I) || Exercise 10.3

00:00:25 Standard Form of Equation of Straight Lines

00:02:52 NCERT Exercise 10.3 Question 1 Reduce the following equations into slope – intercept form and find their slopes and the y – intercepts. (i) x + 7y = 0, (ii) 6x + 3y – 5 = 0, (iii) y = 0.

00:14:22 NCERT Exercise 10.3 Question 2 Reduce the following equations into intercept form and find their intercepts on the axes. (i) 3x + 2y – 12 = 0, (ii) 4x – 3y = 6, (iii) 3y + 2 = 0.

00:25:12 NCERT Exercise 10.3 Question 3 Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.

##### 10(J) || Exercise 10.3

00:00:11 Derivation for Distance between a point and a straight line

00:16:01 NCERT Exercise 10.3 Question 4 Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).

00:22:11 How check lines are parallel through their equations

00:28:31 Derivation for Distance between two parallel lines

00:34:01 NCERT Exercise 10.3 Question 5 Find the points on the x-axis, whose distances from the line x/3+y/4=1 are 4 units.

00:39:11 NCERT Exercise 10.3 Question 6 Find the distance between parallel lines (i) 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0 (ii) l (x + y) + p = 0 and l (x + y) – r = 0.

##### 10(K) || Exercise 10.3

00:00:05 You will need to understand how to make equations and read information from equations before continuing

00:00:55 NCERT Exercise 10.2 Question 7 (Method 1) Find equation of the line parallel to the line 3x-4y+2=0 and passing through the point (-2,3).

00:05:15 NCERT Exercise 10.2 Question 7 (Method 2)

00:08:05 NCERT Exercise 10.2 Question 8 Find equation of the line perpendicular to the line x – 7y + 5 = 0 and having x intercept 3.

00:12:35 NCERT Exercise 10.2 Question 9 Find angles between the lines

00:18:55 NCERT Exercise 10.2 Question 10 The line through the points (h, 3) and (4, 1) intersects the line 7 9 19 0 at right angle. Find the value of h.

00:22:35 NCERT Exercise 10.2 Question 12 Two lines passing through the point (2, 3) intersects each other at an angle of 60o If slope of one line is 2, find equation of the other line.

00:33:25 NCERT Exercise 10.2 Question 13 Find the equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2).

##### 10(L) || Exercise 10.3

00:00:40 NCERT Exercise 10.3 Question 14 (Method 1) Find the coordinates of the foot of perpendicular from the point (–1, 3) to the line 3x – 4y – 16 = 0.

00:08:30 NCERT Exercise 10.3 Question 14 (Method 2)

00:15:10 NCERT Exercise 10.3 Question 15 The perpendicular from the origin to the line y = mx + c meets it at the point (–1, 2). Find the values of m and c.

00:20:20 NCERT Exercise 10.3 Question 16

00:32:50 NCERT Exercise 10.3 Question 17 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

00:40:54 NCERT Exercise 10.3 Question 18 If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that

##### 10(M) || Miscellaneous Exercise

00:00:36 NCERT Exercise 10.3 Question 11

00:03:46 Miscellaneous Exercise Question 1

00:11:06 Miscellaneous Exercise Question 2

00:16:56 Miscellaneous Exercise Question 3 Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and – 6, respectively.

00:21:36 Miscellaneous Exercise Question 4 What are the points on the y-axis whose distance from the line x/3+y/4=1 is 4 units.

00:26:10 Miscellaneous Exercise Question 6 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.

00:32:36 Miscellaneous Exercise Question 7 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.

00:38:46 Miscellaneous Exercise Question 5 Find perpendicular distance from the origin to the line joining the points (cosθ, sin θ) and (cos φ, sin φ).

##### 10(N) || Miscellaneous Exercise

00:00:35 Miscellaneous Exercise Question 8 Find the area of the triangle formed by the lines y – x = 0, x + y = 0 and x – k = 0.

00:07:55 Miscellaneous Exercise Question 9 Find the value of p so that the three lines 3x + y – 2 = 0, px + 2 y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.

00:12:45 Miscellaneous Exercise Question 10

00:23:35 Miscellaneous Exercise Question 11 Find the equation of the lines through the point (3, 2) which make an angle of 45o with the line x – 2y = 3.

00:32:29 Miscellaneous Exercise Question 13 Show that the equation of the line passing through the origin and making an angle θ with the line y=mx+c is y/x = (m ± tan)/ (1∓ m).

00:40:39 Miscellaneous Exercise Question 12 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.

##### 10(O) || Miscellaneous Exercise

00:00:35 Miscellaneous Exercise Question 14 In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?

00:06:36 Miscellaneous Exercise Question 15 Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0.

00:19:16 Miscellaneous Exercise Question 16 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.

00:30:06 Miscellaneous Exercise Question 17 The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (– 4, 1). Find an equation of the legs (perpendicular sides) of the triangle.

00:42:46 Miscellaneous Exercise Question 18 Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the line to be a plane mirror.

00:56:16 Miscellaneous Exercise Question 19 If the lines y = 3x +1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.

##### 10(P) || Miscellaneous Exercise

00:00:25 Miscellaneous Exercise Question 24 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.

00:11:12 Miscellaneous Exercise Question 23

00:24:35 Miscellaneous Exercise Question 22 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.

00:33:46 Miscellaneous Exercise Question 21 Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.

00:43:35 Miscellaneous Exercise Question 20 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.

##### 10(Q) || Miscellaneous Examples

00:00:18 Chapter 10 Miscellaneous Example 20 If the lines 2x+y-3=0, 5x+ky-3=0 and 3x-y-2=0 are concurrent, find the value of k.

00:04:08 Chapter 10 Miscellaneous Example 21 Find the distance of the line 4x – y = 0 from the point P (4, 1) measured along the line making an angle of 135° with the positive x-axis.

00:12:38 Chapter 10 Miscellaneous Example 22 Assuming that straight lines work as the plane mirror for a point, find the image of the point (1, 2) in the line x – 3y + 4 = 0.

00:22:28 Chapter 10 Miscellaneous Example 23

00:31:28 Chapter 10 Miscellaneous Example 24 A line is such that its segment between the lines 5x – y + 4 = 0 and 3x + 4y – 4 = 0 is bisected at the point (1, 5). Obtain its equation.

00:46:08 Chapter 10 Miscellaneous Example 25 Show that the path of a moving point such that its distances from two lines 3x – 2y = 5 and 3x + 2y = 5 are equal is a straight line.

##### 10(R) || Supplementary Exercise

00:00:05 Equation of Family of lines passing through the point of intersection of two lines with examples and animation

00:19:00 NCERT Supplementary Exercise 10.4 Chapter 10 Question 1 Find the equation of line through the intersection of lines 3x+4y=7 and x-y+2=0 and whose slope is 5.

00:25:45 NCERT Supplementary Exercise 10.4 Chapter 10 Question 2 Find the equation of line through the intersection of lines c+2y-3=0 and 4x-y+7=0 and which is parallel to 5x+4y-20=0

00:29:23 NCERT Supplementary Exercise 10.4 Chapter 10 Question 3 Find the equation of line through the intersection of lines 2x+3y-4=0 and x-5y=7 that has x-intercept equal to -4.

00:33:02 NCERT Supplementary Exercise 10.4 Chapter 10 Question 4 Find the equation of line through the intersection of lines 5x-3y=1 and 2x+3y-23=0 and perpendicular to the line 5x-3y-1=0.

##### 10(S) || Supplementary Exercise

00:00:01 Purpose of coordinate axes

00:00:54 Geometric Shapes follows “rigid body motion”

00:02:40 All equations have two information related to geometric shapes

00:04:00 Geometrical proof for benefits of shifting of origin

00:08:06 Transformation or translation of axes has two parts : shifting of origin and rotation of axes

00:09:16 Derivation for relation between new origin, old coordinate and new coordinate NCERT Supplementary Exercise 10.5

00:14:56 Question 1

00:20:35 Question 2