# Summary

• The roots of a quadratic equation can be found using the formula:

• For the equation ax 2 + bx + c = 0, we have x2â€“ (sum of roots) x + (product of roots) = 0
• Distance between two points A(x1, y1) and B(x2, y2) is given by

• The coordinates of a point P, which divides the line joining two points A(x1, y1) and B(x2, y2) in the ratio m:n is given as

• The midpoint of the line joining two points A(x1, y1) and B(x2, y2) is given by

• The centroid G(x, y) of a âˆ† ABC with vertices A(x1, y1), B(x2, y2) and C(x3, y3) is given by

• Area of a âˆ† is given by  Sq.units
• If three points
• If A(x1, y1) and B(x2, y2) are two points, then the ratio  gives the slope of the line joining the point AB.
• Let m1 and m2 be the slopes of two lines, then
• m1 = m2, if the lines are parallel
• = â€“1, if the lines are perpendicular
• Equations of a line:
• Point-slope form of line is given by ( y â€“ y1) = m (x â€“ x1).
• 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 a1x + b1 y + c1 = 0 can be written as ax + by + c + k (a1x + b1 y + c1) = 0, where k is any constant.