LECTURE 1 STRAIGHT LINE

Cartesian Coordinate System
A Cartesian plane consists of two perpendicular lines called the x-axis (horizontal) and the y-axis (vertical).
The point where these axes intersect is called the origin, denoted by O(0,0)
Every point in the plane is represented by an ordered pair (x,y), where: x is the abscissa (horizontal distance from the y-axis) and y is the ordinate (vertical distance from the x-axis).
Quadrants in the Cartesian Plane
The Cartesian plane is divided into four quadrants based on the signs of the coordinates (x,y)
First Quadrant: (+x,+y)
Second Quadrant: (-x,+y)
Third Quadrant: (-x,-y)
Fourth Quadrant: (+x,-y)
Section Formula: - If a point P(x,y) divides a line segment joining points A(x1,y1) and B(x2,y2) in the ratio m:n, then the coordinates of P are:
For internal division : X = m1x2+m2x1/m1+m2, y = m1y2+m2y1/m1+m2
For external division : X = m1x2-m2x1/m1-m2, y = m1y2-m2y1/m1-m2
Midpoint Formula: - The midpoint M(x,y) of a line segment joining points A(x1,y1) and B(x2,y2) is given by: x = (x1+x2)/2 y = (y1+y2)/
Centroid of a Triangle: - The centroid of a triangle is the point where its three medians intersect. The coordinates of the centroid G(x,y) for a triangle with vertices A(x1,y1), B(x2,y2) and C(x3,y3) are: x = (x1+x2+x3)/3, y = (y1+y2+y3)/3
Area of a Triangle: - The area of a triangle formed by three points A(x1,y1), B(x2,y2) and C(x3,y3) is: Area = 12∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣.
Collinearity of Points: - Three points A(x1,y1), B(x2,y2) and C(x3,y3) are collinear if the area of the triangle formed by them is zero:
Equation of a Horizontal and Vertical Line
The equation of a horizontal line (parallel to the x-axis) at y=c is: y=c
The equation of a vertical line (parallel to the y-axis) at x=c is: x=c
Here are the important facts and formulas from the Straight Line chapter of Class 11
Slope of a Line: - The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by: m = {y2 - y1}/{x2 - x1)
Slope of a line parallel to the x-axis is 0.
Slope of a line parallel to the y-axis is undefined.
Forms of a Straight Line: -
Slope-Intercept Form: - The equation of a line with slope m and y-intercept c is: y = mx + c
Point-Slope Form: - The equation of a line passing through point (x1, y1) with slope m is: - y - y1 = m(x - x1)
Two-Point Form: - The equation of a line passing through two points (x1, y1) and (x2, y2) is: - y - y1 = {y2 - y1}(x - x1)/(x2 - x1)
Intercept Form: - The equation of a line making intercepts a on the x-axis and b on the y-axis is: - x/a + y/b = 1
Normal Form: - The equation of a line at a perpendicular distance p from the origin, with angle of inclination alpha, is: xcos(alpha) + ysin(alpha) = p.
General Equation of a Line: - The general form of a line is: Ax + By + C = 0
where A, B, and C are constants.
Angle Between Two Lines: - The angle (theta) between two lines with slopes m1 and m2 is given by: tan(theta) = m2 - m1/1 + m1 m2}
If m1.m2 = -1, the lines are perpendicular.
Condition for Parallel and Perpendicular Lines: -
Parallel Lines: - Two lines with slopes m1 and m2 are parallel if: m1 = m2
Perpendicular Lines: - Two lines with slopes m1 and m2 are perpendicular if:
m1.m2 = -1
Distance Between Two Points: - The distance d between two points (x1, y1) and (x2, y2) is given by: d = sqrt{(x2 - x1)^2 + (y2 - y1)^2
Distance of a Point from a Line: - The perpendicular distance d of a point (x1, y1) from the line Ax + By + C = 0 is given by: d = {|Ax1 + By1 + C|}/sqrt{A^2 + B^2}
Distance Between Two Parallel Lines: - The distance d between two parallel lines Ax + By + C1 = 0 and Ax + By + C2 = 0 is: d = {|C1 - C2|}/{sqrt{A^2 + B^2}
Collinearity of Three Points: - Three points (x1, y1), (x2, y2), and (x3, y3) are collinear if the area of the triangle formed by them is zero, i.e.
Area = (1/2) |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| = 0
Equation of a Line Parallel or Perpendicular to a Given Line: -
Parallel Line: - The equation of a line parallel to Ax + By + C = 0 is: Ax + By + C' = 0
Perpendicular Line: - The equation of a line perpendicular to Ax + By + C = 0\) is: Bx - Ay + C'' = 0
Straight Line Class 11 Notes
Straight Line Class 11 Formulas
Straight Line Class 11 NCERT Solutions
Straight line chapter in the NCERT Class 11 Maths book.
Straight Line Class 11 Important Questions
Straight Line Class 11 Solved Examples
Straight Line Class 11 Practice Questions
Straight Line Class 11 Video Lectures
Instagram I’d: www.instagram....
Telegram channel: - t.me/youtube_g...
Facebook page: - www.facebook.c...
Email Id: - [e-mail]
Whatsapp No: - 9528824424