# Straight Lines Class 11

Straight Lines class 11 – If $\theta$ is the inclination of a line l, then the slope of a line is given by tan θ. It is denoted by ‘m’. The slope of a line is not defined if it has 90 degree inclination. Thus, $m \;=\; tan \theta , \;θ \neq 90$. Also, the slope of x axis is 0 and not defined for y axis. The acute angle between two lines $L_{1}\;and\;L_{2}$ with slopes $m_{1}\;and\;m_{2}$ is given by

$tan\theta =\left | \frac{m_{2}-m_{1}}{1+m_{1}m_{2}} \right |$

The obtuse angle can be found by using $\phi =180-\theta$. 3 points A,B, and C are said to be collinear if slope of AB and BC are equal. The point (x, y) lies on the line if its coordinates satisfy the equation: $y–y_{0} = m(x–x_{0})$ where m = slope through the fixed point $\left ( x_{0} ,y_{0}\right )$.

The equation of line whose intercept on x axis is ‘a’ and intercept on y axis is ‘b’ is given by: $\frac{x}{a}+\frac{y}{b}=1$

The perpendicular distance of a line Ax + By+ C = 0 from a point $\left ( x_{1},y_{1}\right )$ is given by:

$d=\frac{\left | Ax_{1}+By_{1}+c \right |}{\sqrt{A^{2}+B^{2}}}$

The Distance between two parallel lines $Ax+By+C_{1}=0$ and $Ax+By+C_{1}=0$ is given by:

$d=\frac{\left | C_{1}-C_{2} \right |}{\sqrt{A^{2}+B^{2}}}$

### Straight Lines class 11 Examples

#### Practise This Question

If p(qr) is false, then the truth values of p,q,r are respectively