Math Assignment Class VIII | Square & Square Root

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Straight Lines Class XI Chapter 10
Basic concepts of straight line chapter 10 standard XI, slope of the line, different forms of equation of lines and general equation of line.
The angle θ made by the line l with positive direction of x- axis and measured anti-clockwise is called the angle of inclination of the line
Angle of inclination of the x-axis is 0o. Angle of inclination of all the lines parallel to the x- axis is also 0o.
Angle of
inclination of the y-axis is 90o.
Angle of inclination of all the lines parallel to the y- axis is also 90o.
Slope of
the line
If 'θ' is the angle of inclination of the line l then tanθ is called the slope or gradient of the line l. Slope is denoted by m
Therefore slope of line l = m = tanθ
Slope of x-axis = tan0 = 0
Slope of y - axis = tan90o = ∞ or undefined
Slope of the line passing through the two points P(x1, y1), and Q(x2, y2)
\[m=tan\theta =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]Two lines are parallel if their slopes are equal or m1 = m2
If a line is above the x-axis then choose +ve sign and if a line below the x-axis then choose –ve sign.
Point Slope form of equation of line
This is also known as one point form of equation of line.
Let a line L with slope m passes through the point Q(x1, y1). If P(x, y) is any arbitrary point on the line L, Then equation of line is given by
y - y1 = m(x - x1) where
\[m=tan\theta =\frac{y-y_{1}}{x-x_{1}}\]
Two Point form of equation of line
Let a line L passing through two points P(x1, y1) and Q(x2, y2). Slope m of the line is given by \[m=tan\theta =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]. If R(x, y) is any arbitrary point on the line then equation of the line is given by \[y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})\]Slope intercept form of equation of line
Let a line L with slope m cut the y-axis at a distance c from the origin at point (0, c). Then c is called the y-intercept of the line. If P(x, y) is any arbitrary point on the line then equation of the line is given by
y - c = m(x - 0) ⇒ y = mx + c
If line L with slope m cut the x-axis at a distance c from the origin at point (c, 0). Then c is called the x-intercept of the line. If P(x, y) is any arbitrary point on the line then equation of the line is given by
y - 0 = m(x - c) ⇒ y = m(x + c)
Intercept form of equation of line
Let L is a line which make intercept a on the x-axis and intercept b on y-axis, then slope of the line is given by \[Slope(m)=\frac{b-0}{0-a}=\frac{-b}{a}\]Equation of line is given by\[y-0=\frac{-b}{a}(x-a)\]\[ay=-bx+ab\]\[ay+bx=ab\]\[\frac{ay}{ab}+\frac{bx}{ab}=\frac{ab}{ab}\]\[\frac{y}{b}+\frac{x}{a}=1\]\[\frac{x}{a}+\frac{y}{b}=1\]This equation is called the intercept form of equation of line.
Normal form of equation of line
Let L is a line whose perpendicular distance from the origin is p and perpendicular OA makes an angle θ with the x-axis measured anti-clockwise direction, then Normal form of the equation of line is given by
xcosθ + ysinθ = p
ax + by + c1 = 0,
ax + by + c2 = 0
\[d=\left | \frac{c_{1}-c_{2}}{\sqrt{a^{2}+b^{2}}} \right |\]
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