Line Formula

Distance formula:

• d = √[(x2 – x1)² + (y2 – y1)²]

Section Formula:

• x = (mx2 + nx1)/(m + n)
• y = (my2 + ny1)/(m + n)

Centroid:

• G = [(x1 + x2 + x3)/3, (y1 + y2 + y3)/3]

Incentre:

• I = {(ax1 + bx2 + cx3)/(a + b + c), (ay1 + by2 + cy3) / (a + b + c)}

Excentre:

• I1 = {(-ax1 + bx2 + cx3)/(-a + b + c), (-ay1 + by2 + cy3)/(-a + b + c)}

Slope formula:

• m = (y1 – y2) / (x1 – x2)
• Slope of a line ax + by + c = 0 is -coefficient of x/coefficient of y = -a/b

Equation of a straight line in various forms:

• Point Slope form: y – y1 = m(x – x1)
• Slope intercept form: y = mx + c
• Two point form: y – y1 = {(y2 – y1) / (x2 – x1)} × (x – x1)
• Intercept form: (x/a) + (y/b) = 1
• Perpendicular / Normal form: x cos α + y sin α = p
• Parametric form: x = x1+ r cos θ , y = y1 + r sin θ
• Symmetric form: (x – x1)/cos θ = (y – y1) / sin θ = r) General form: ax + by + c = 0
• L1 = a1x + b1y + c1 = 0 and L2 = a2x + b2y + c2 = 0 is given by L1 + kL2 = 0