Class 11 Math Chapter 9 Straight Lines Notes (Short & Handwritten Notes)

BoardStudy given Class 11 Math Chapter 9 Straight Lines notes according to latest NCERT syllabus to make your study more convenient and easy. We have covered every topic in a simple and easy way so anyone can understand the chapter and perform well in the exam.

Notes are very clean and colourful written by BoardStudy subject matter experts. Every important concept, formula, diagram and derivation is shared in the Straight Lines notes that will help you solve the problem. By reviewing these notes regularly you will master the Straight Lines chapter and can score well in exam.

Class 11 Math Straight Lines Notes

Chapter 8: Sequences and Series Notes
Chapter 10: Conic Sections Notes

Key Points Straight Lines

Straight Lines

Distance between the points $P(x_1, y_1)$ and $Q(x_2, y_2)$ is$$PQ = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}$$

The coordinates of the point which divides the join of $(x_1, y_1)$ and $(x_2, y_2)$ in the ratio $m:n$

Internally is

Externally is

Midpoint of the join of $(x_1, y_1)$ and $(x_2, y_2)$ is

Area of the triangle

Area of the triangle whose vertices are
$(x_1, y_1), (x_2, y_2), (x_3, y_3)$ is

If the area of triangle ABC is 0, then three points A, B and C lie on a line i.e., they are collinear.

Centroid of triangle

The coordinates of centroid of the triangle are$$\left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$$

Straight Line

General equation of line is$$ax + by + c = 0$$

Slope or Gradient of line (m)

The inclination of angle $\theta$θ to a line with positive direction of x-axis in the anticlockwise direction, the tangent of angle $\theta$θ is said to be slope of a line.$$m = \tan\theta = \frac{y_2 – y_1}{x_2 – x_1}$$

NOTE:

• Slope of a line parallel to X-axis is zero.
• Slope of a line parallel to Y-axis is not defined.

If two lines are parallel, their slopes are equal$$m_1 = m_2$$

If two lines are perpendicular to each other, then their product of slopes is −1$$m_1 m_2 = -1$$

Collinearity of three points

If A, B & C are three points in the XY plane, then they will lie on a line i.e., three points are collinear if and only if$$\text{slope of } AB = \text{slope of } BC$$

Various forms of the equation of a line

Horizontal & Vertical lines

If a line is at a distance $a$a and parallel to X-axis, then the equation of the line is$$y = \pm a$$

If a line is at a distance $b$b and parallel to Y-axis, then the equation of the line is$$x = \pm b$$