A straight line is a curve such that every point on the line segment joining any two points on it lies on it.
every first degree equation in x,y represents a straight line.
Showing posts with label Straight line. Show all posts
Showing posts with label Straight line. Show all posts
Sunday, December 7, 2008
Slope (Gradient) of a straight line
The general equation of a line is of the form ax +by +c = o and its slope is –a/b, provided b≠0.
Anlge between two straight lines
If m1 and m2 are the slopes of two lines, then the acute angle θ between them is given by tan θ = |m1-m2|/|1 + m1*m2|, provided m1*m2≠-1.
Intercepts of a line on the axes
If a straight line cuts x axis at A and O is origin AO or OA is the x-intercept.
If a straight line cuts y axis at B and O is origin BO or OB is the y-intercept.
If a straight line cuts y axis at B and O is origin BO or OB is the y-intercept.
Friday, November 7, 2008
IIT JEE Study Guide 13. Cartesian System of Coordinates and Straight Lines - Revision Facilitator
1. Introduction
2. Catesian coordinate system
3. Distance between two points
4. Area of a triangle
5. Section Formulae
6. coordinates of the centroid, in-centre, and ex centre of a triangle
7. Locus and equation to a locus
8. Shifting of origin
9. Rotation of axes
10. Definition of a straight line
11. Slope (Gradient) of a straight line
12. Angle between two straight lines
13. Intercepts of a line on the axes
14. Equations of lines parallel to the coordinate axes
15. Different forms of the equation of a straight line
16. Transformation of general equation in different standard forms
17. point of intersection of two lines
18. Coordination of concurrency of three lines
19. Lines parallel and perpendicular to a given line
20. Angle between two straight lines when their equations are given.
21. Distance of a point from a line
22. Positions of points relative to a line
23. Equations of straight lines passing through a given point and making a given angle with a given line
24. Equations of the bisectors of the angles between two straight lines
25. Some important points of a triangle
26. Family of lines through the intersection of two given lines
Study Plan
Day 1
1. Introduction
2. Catesian coordinate system
3. Distance between two points
Day 2
4. Area of a triangle
5. Section Formulae
6. coordinates of the centroid, in-centre, and ex centre of a triangle
Day 3
7. Locus and equation to a locus
8. Shifting of origin
Day 4
9. Rotation of axes
10. Definition of a straight line
11. Slope (Gradient) of a straight line
12. Angle between two straight lines
Day 5
13. Intercepts of a line on the axes
14. Equations of lines parallel to the coordinate axes
15. Different forms of the equation of a straight line
Day 6
16. Transformation of general equation in different standard forms
17. point of intersection of two lines
18. Coordination of concurrency of three lines
Day 7
19. Lines parallel and perpendicular to a given line
20. Angle between two straight lines when their equations are given.
21. Distance of a point from a line
Day 8
22. Positions of points relative to a line
23. Equations of straight lines passing through a given point and making a given angle with a given line
Day 9
24. Equations of the bisectors of the angles between two straight lines
25. Some important points of a triangle
26. Family of lines through the intersection of two given lines - Up to Example 10
Day 10
26. Family of lines through the intersection of two given lines - Examples 21 to 30
Day 11
Illustrative Objective Type Examples 1 to 19
Day 12
Objective Type Exercise 1 to 20
Day 13
O.T.E. 21 to 40
Day 14
O.T.E. 41 to 60
Day 15
O.T.E. 61 to 80
Revision Period - 30 minutes a day
Day 16
O.T.E. 81 to 90
Day 17
O.T.E. 91 to 100
Day 18
O.T.E. 101 to 110
Day 19
O.T.E. 111 to 120
Day 20
O.T.E. 121 to 130
Day 21
O.T.E. 131 to 142
Day 22
Fill in the blanks type exercise 1 to 10
Day 23
Fill in the blanks type exercise 11 to 20
Day 24
Fill in the blanks type exercise 21 to 30
Day 25
Fill in the blanks type exercise 31 to 40
Day 26
True of False Exercise 1 to 19
Day 27
Practice Exercise 1 to 10
Day 28
Practice Exercise 11 to 20
Day 29
Practice Exercise 21 to 30
Day 30
31 to 41
Should you compulsorily do every problem. Not necessary. If you feel, you know how to do it, you can always skip some problems. But make a note of all difficult problems. You may have to a relook at them sometimes more to remember the complication or complexity in that problem.
Try to recollect relevant points on the topic.
If required right click on the topic and click on open in a new window to read the relevant material.
Close the window and come back.
Euclidean Geometry and Analytic Geometry - Difference
Distance between two points
Area of a triangle
Section Formulae
coordinates of the centres related to triangle
Definition of a straight line
Slope (Gradient) of a straight line
Angle between two straight lines
Intercepts of a line on the axes
Joint equation of a pair of straight lines
2. Catesian coordinate system
3. Distance between two points
4. Area of a triangle
5. Section Formulae
6. coordinates of the centroid, in-centre, and ex centre of a triangle
7. Locus and equation to a locus
8. Shifting of origin
9. Rotation of axes
10. Definition of a straight line
11. Slope (Gradient) of a straight line
12. Angle between two straight lines
13. Intercepts of a line on the axes
14. Equations of lines parallel to the coordinate axes
15. Different forms of the equation of a straight line
16. Transformation of general equation in different standard forms
17. point of intersection of two lines
18. Coordination of concurrency of three lines
19. Lines parallel and perpendicular to a given line
20. Angle between two straight lines when their equations are given.
21. Distance of a point from a line
22. Positions of points relative to a line
23. Equations of straight lines passing through a given point and making a given angle with a given line
24. Equations of the bisectors of the angles between two straight lines
25. Some important points of a triangle
26. Family of lines through the intersection of two given lines
Study Plan
Day 1
1. Introduction
2. Catesian coordinate system
3. Distance between two points
Day 2
4. Area of a triangle
5. Section Formulae
6. coordinates of the centroid, in-centre, and ex centre of a triangle
Day 3
7. Locus and equation to a locus
8. Shifting of origin
Day 4
9. Rotation of axes
10. Definition of a straight line
11. Slope (Gradient) of a straight line
12. Angle between two straight lines
Day 5
13. Intercepts of a line on the axes
14. Equations of lines parallel to the coordinate axes
15. Different forms of the equation of a straight line
Day 6
16. Transformation of general equation in different standard forms
17. point of intersection of two lines
18. Coordination of concurrency of three lines
Day 7
19. Lines parallel and perpendicular to a given line
20. Angle between two straight lines when their equations are given.
21. Distance of a point from a line
Day 8
22. Positions of points relative to a line
23. Equations of straight lines passing through a given point and making a given angle with a given line
Day 9
24. Equations of the bisectors of the angles between two straight lines
25. Some important points of a triangle
26. Family of lines through the intersection of two given lines - Up to Example 10
Day 10
26. Family of lines through the intersection of two given lines - Examples 21 to 30
Day 11
Illustrative Objective Type Examples 1 to 19
Day 12
Objective Type Exercise 1 to 20
Day 13
O.T.E. 21 to 40
Day 14
O.T.E. 41 to 60
Day 15
O.T.E. 61 to 80
Revision Period - 30 minutes a day
Day 16
O.T.E. 81 to 90
Day 17
O.T.E. 91 to 100
Day 18
O.T.E. 101 to 110
Day 19
O.T.E. 111 to 120
Day 20
O.T.E. 121 to 130
Day 21
O.T.E. 131 to 142
Day 22
Fill in the blanks type exercise 1 to 10
Day 23
Fill in the blanks type exercise 11 to 20
Day 24
Fill in the blanks type exercise 21 to 30
Day 25
Fill in the blanks type exercise 31 to 40
Day 26
True of False Exercise 1 to 19
Day 27
Practice Exercise 1 to 10
Day 28
Practice Exercise 11 to 20
Day 29
Practice Exercise 21 to 30
Day 30
31 to 41
Should you compulsorily do every problem. Not necessary. If you feel, you know how to do it, you can always skip some problems. But make a note of all difficult problems. You may have to a relook at them sometimes more to remember the complication or complexity in that problem.
Try to recollect relevant points on the topic.
If required right click on the topic and click on open in a new window to read the relevant material.
Close the window and come back.
Euclidean Geometry and Analytic Geometry - Difference
Distance between two points
Area of a triangle
Section Formulae
coordinates of the centres related to triangle
Definition of a straight line
Slope (Gradient) of a straight line
Angle between two straight lines
Intercepts of a line on the axes
Joint equation of a pair of straight lines
Saturday, June 7, 2008
Ch.13 Straight Lines - Revision Points 1
1. The equation of a line parallel to x-axis is of the form y = k.
The equation of a line parallel to y axis is of the form x = k, where k is a constant.
2. If a line makes an angle θ with the positive direction of x-axis and θ ≠π/2, then the slope of the line is given by tan θ.
3. the slope of a line passing through (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1), provided x1≠x2.
4. If two lines have finite slopes m1 and m2
then they are parallel iff m1 = m2
they are perpendicular iff m1*m2 = -1
5. The equation of a line having slope m and y intercept c is y = mx+c
6. The equation of a line having slope m and passing through (x1,y1) is
(y-y1) = m(x-x1)
7. The equation of a line having slope m and passing through (x1,y1)and (x2,y2) is
(y-y1)/(x-x1) = (y1-y2)/(x1-x2)
8.The equation of a line making non-zero intercepts and b on the x and y axes respectively is
(x/a) + (y/b) = 1
9. The equation of a line such that the perpendicular drawn from the origin to the line has length p and inclination α is
x cos α + y sin α = p.
10. The general equation of a line is of the form ax +by +c = o and its slope is –a/b, provided b≠0.
11. If m1 and m2 are the slopes of two lines, then the acute angle θ between them is given by tan θ = |m1-m2|/|1 + m1*m2|, provided m1*m2≠-1.
12. The perpendicular distance of (x1,y1) from the line ax+by+c = 0 is given by |ax1 + by1 + c|/| √(a² + b²)|
13. The point of intersection of two lines, which are not parallel, can be found by solving their equations simultaneously.
14. Family of lines
If u ≡ a1x + b1y +c1 = 0 and
v≡ a2x +b2y +c2 = 0
the u + kv = 0, k Є R represents a family of lines
(i) if u and v are intersecting lines, then u + kv = 0, k Є R represents a family of lines passing through the point of intersection of u =0 and v=0.
(ii) if u and v are two parallel lines, u + kv = 0, k Є R represents a family of straight lines parallel to u =0 and v=0.
The equation of a line parallel to y axis is of the form x = k, where k is a constant.
2. If a line makes an angle θ with the positive direction of x-axis and θ ≠π/2, then the slope of the line is given by tan θ.
3. the slope of a line passing through (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1), provided x1≠x2.
4. If two lines have finite slopes m1 and m2
then they are parallel iff m1 = m2
they are perpendicular iff m1*m2 = -1
5. The equation of a line having slope m and y intercept c is y = mx+c
6. The equation of a line having slope m and passing through (x1,y1) is
(y-y1) = m(x-x1)
7. The equation of a line having slope m and passing through (x1,y1)and (x2,y2) is
(y-y1)/(x-x1) = (y1-y2)/(x1-x2)
8.The equation of a line making non-zero intercepts and b on the x and y axes respectively is
(x/a) + (y/b) = 1
9. The equation of a line such that the perpendicular drawn from the origin to the line has length p and inclination α is
x cos α + y sin α = p.
10. The general equation of a line is of the form ax +by +c = o and its slope is –a/b, provided b≠0.
11. If m1 and m2 are the slopes of two lines, then the acute angle θ between them is given by tan θ = |m1-m2|/|1 + m1*m2|, provided m1*m2≠-1.
12. The perpendicular distance of (x1,y1) from the line ax+by+c = 0 is given by |ax1 + by1 + c|/| √(a² + b²)|
13. The point of intersection of two lines, which are not parallel, can be found by solving their equations simultaneously.
14. Family of lines
If u ≡ a1x + b1y +c1 = 0 and
v≡ a2x +b2y +c2 = 0
the u + kv = 0, k Є R represents a family of lines
(i) if u and v are intersecting lines, then u + kv = 0, k Є R represents a family of lines passing through the point of intersection of u =0 and v=0.
(ii) if u and v are two parallel lines, u + kv = 0, k Є R represents a family of straight lines parallel to u =0 and v=0.
Subscribe to:
Posts (Atom)