EduRev's Tip:
Slope(m) of a line is the tangent of the angle made by the line with the positive direction of the XAxis.
For a general equation ax + by + c = 0; slope (m) = a/b.
For a line joining two points, P (x_{1},y_{1}) and Q(x_{2},y_{2}), the slope(m) is =
Equation of a line parallel to Xaxis is y = a {Of XAxis is y = 0}
Equation of a line parallel to YAxis is x = a {Of YAxis is x = 0}
The intercept of a line is the distance between the point where it cuts the XAxis or YAxis and the origin. YIntercept is often denoted with the letter ‘c’.
Equation of a line
General form: ax + by + c = 0
Slope Intercept Form: Slope is m, yintercept is c
⇒ y = mx + c
Slope Point Form: Slope is m, point is x_{1},y1
⇒ y – y_{1} = m(x – x_{1})
Two Point Form: Two points are x_{1},y_{1} and x_{2},y_{2}
⇒
Two Intercept Form: Xintercept is a, Yintercept is b.
⇒ OR bx + ay = ab
A cute angle between two lines with slope m_{1} and m_{2} is given by
⇒
⇒ For parallel lines, θ = 0°; m_{1} = m_{2}
⇒ For parallel lines, θ = 90°; m_{1}m_{2} = 1
Distance of a point P (x_{1},y_{1}) from a line ax + by + c = 0
⇒
⇒ From origin, d =
Distance between two parallel lines, ax + by + c_{1} = 0 and ax + by + c_{2} = 0
⇒
EduRev's Tip: If we know three points A(x_{1},y_{1}), B(x_{2},y_{2} ) and C(x_{2},y_{2}) of a parallelogram, the fourth point is given by
⇒ (x_{1} + x_{3} – x_{2}, y_{1} + y_{3} – y_{2})
Triangle
The vertices are P (x_{1},y_{1}), Q(x_{2},y_{2}) and R(x_{3},y_{3})
Incenter
Centroid =
Area = ½ [ x_{1}(y_{2} – y_{3}) + x_{2} (y_{3} – y_{1}) + x_{3} (y_{1} – y_{2})]
Circle
General Equation: x^{2} + y^{2} + 2gx + 2fy + c = 0
⇒ Centre is (g, f) and radius =
Centre is (h, k) and radius is r
⇒
Centre is origin and radius is r
⇒ x^{2} + y^{2} = r^{2}
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1. What are the formulas for finding the distance between two points in coordinate geometry? 
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3. What is the formula for finding the slope of a line in coordinate geometry? 
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