# Summary

- The roots of a quadratic equation can be found using the formula:
- For the equation ax
^{2}+ bx + c = 0, we have x^{2}â€“ (sum of roots) x + (product of roots) = 0 - Distance between two points A(x
_{1}, y_{1}) and B(x_{2}, y_{2}) is given by - The coordinates of a point P, which divides the line joining two points A(x
_{1}, y_{1}) and B(x_{2}, y_{2}) in the ratio m:n is given as - The midpoint of the line joining two points A(x
_{1}, y_{1}) and B(x_{2}, y_{2}) is given by - The centroid G(x, y) of a âˆ† ABC with vertices A(x
_{1}, y_{1}), B(x_{2}, y_{2}) and C(x_{3}, y_{3}) is given by - Area of a âˆ† is given by Sq.units
- If three points
- If A(x
_{1}, y_{1}) and B(x_{2}, y_{2}) are two points, then the ratio gives the slope of the line joining the point AB. - Let m
_{1}and m_{2}be the slopes of two lines, then- m
_{1}= m_{2}, if the lines are parallel - = â€“1, if the lines are perpendicular

- m
- Equations of a line:
- Point-slope form of line is given by ( y â€“ y
_{1}) = m (x â€“ x_{1}). - Two points form a line is given by
- Intercept form of a line is given by
- General form of the equation of a line is given by ax + by + c = 0
- The equation of a line passing through the point of intersection of the lines ax + by + c = 0 and a
_{1}x + b_{1 }y + c_{1}= 0 can be written as ax + by + c + k (a_{1}x + b_{1 }y + c_{1}) = 0, where k is any constant.

- Point-slope form of line is given by ( y â€“ y