Plus One Maths Notes Chapter 10 Straight Lines is part of Plus One Maths Notes. Here we have given Kerala Plus One Maths Notes Chapter 10 Straight Lines.

Board | SCERT, Kerala |

Text Book | NCERT Based |

Class | Plus One |

Subject | Maths Notes |

Chapter | Chapter 10 |

Chapter Name | Straight Lines |

Category | Plus One Kerala |

## Kerala Plus One Maths Notes Chapter 10 Straight Lines

- Distance between the two point (x
_{1}, y_{1}) and (x_{2}, y_{2}) is

**OR**

- The coordinates of a point dividing the line segment joining (x
_{1}, y_{1}) and (x_{2}, y_{2}) in the ratio m:n internally are

- In the case of external division, coordinates

- Midpoint of the line joining (X
_{1}, y_{1}) and (x_{2},y_{2}) is

- X – axis divides the line segment joining (x
_{1}, y_{1}) and (x_{2}, y_{2}) in the ratio is y_{1}: y_{2 }(y_{1}≠ y_{2}) - Y – axis divided the line segment joining in the ratio is x
_{1}: x_{2}(x_{1 }≠ x_{2}) - Area of a triangle ABC whose vertices are

- Centroid of ΔABC is

- InCentre of ΔABC is
- where a, b and c are length of sides BC, AC and AB.

**Slope of a Line (m)**

- If the angle made by the line with the positive direction of x-axis measured in the anti clockwise direction (inclination) is θ, then the slope of the line is tan θ.
- Slope of x-axis and any line parallel to x- axis is zero (tan 0 = 0).
- Slope of y-axis and any line parallel to y- axis is not defined (tan 90° is not defined).
- Slope is positive if θ is acute (θ< 90°)
- Slope is negative if θ is obtuse (θ >90°)
- Slope of the line joining (x
_{1},y_{1}) and (x_{2},y_{2}) is

- If two non vertical lines are parallel their slopes are equal (m
_{1}= m_{2}) - If two non vertical lines are perpendicular product of their slopes is -1 (m
_{1}_{ }m_{2}= -1) - Three points A, B and C are collinear if slope of AB = slope of BC.

**Equation of a Line in Different Forms**

- Equation of any line parallel to and above x-axis is y = b

(‘b’ is the distance of the line from x- axis) Equation of x-axis is y = 0

If the line is parallel and below the x-axis, equation is y = -b - Equation of any line parallel to y-axis is x = a (right of y-axis)

(‘a’ is the distance of the line from y- axis)

Equation of y-axis is x = 0

If the line is on the left side of y-axis, its equation is x = – a - Equation of a line through origin and having slope ‘m’ is y = mx
- Equation of a line through (x, y
_{1}) and having slope m is y – y_{1}= m(x – x_{1}) - Equation of a vertical line through (x
_{1}, y_{1}) is x= x, - Equation of a horizontal line through (x
_{1}, y_{1}) is y = y_{1 } - Equation of a line with slope ‘m’ and cutting off an intercept c on y-axis is

y = mx + c - Equation of a line cutting off intercepts ‘a’and ‘b’from the x-axis and y-axis respectively is

.If a line with slope m makes x-intercept d, then equation of the line is y = m (x – d)] - Equation of a line through the points (x
_{1}, y_{1}) and (x_{2}, y_{2}) is

- Equation of a line passing through the point (x
_{1}, y) and inclined at an angle 0 to the positive direction of x-axis is

- x = x + r cos 0, y = y1+ r sin 0 is the parametric equation of the line (r- parameter) for different values of ‘r’ we can find different points on the line.
- Equation of a line which is ‘p’ units away from origin and whose perpendicular from origin makes an angle ‘ω’ with positive x-axis is: x cos ω + y sin ω = p.
- General form of the equation of a straight line is ax + by + c = 0
- If m
_{1,}m_{2}are the slopes of two lines, then the acute angle between them is given

- Slope of the line ax + by + c = 0 is

i.e., - Lines a
_{1}x + b_{1}y + c_{1}= 0 and a_{2}x + b_{2}y + c_{2 }= 0, are parallel if , are perpendicular if

a_{1}a_{2}+ b_{1}b_{2}= 0 and perpendicular distance from the point (x_{1}, y_{1}) to the line.

**Family of Straight Lines**

- Parallel to the line ax + by + c = 0 is ax + by + k = 0
- Perpendicular to the line ax + by + c = 0 is bx – ay + k = 0
- Family of straight lines passing through the intersection of the lines

a_{1}x + b_{1}y + c_{1}= 0 and a_{2}x + b_{2}y + c_{2}= 0 is

a_{1}x + b_{1}y + c_{1}+ k (a_{2}x + b_{2}y + c_{2}) = 0

**Concurrent Lines**

- To find the point of intersection of two lines, solve their equations.
- The lines a
_{1}x + b_{1}y + c_{1}= 0,

a_{2}x + b_{2}y + c_{2}= 0 and

a_{3}x + b_{3}y + c3 = 0 and

- Distance between parallel lines ax + by + c
_{1}= 0 and ax + by + c_{2}= 0 is given by

We hope the Plus One Maths Notes Chapter 10 Straight Lines help you. If you have any query regarding Kerala Plus One Maths Notes Chapter 10 Straight Lines, drop a comment below and we will get back to you at the earliest.