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

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