⁦Dividing a segment in a ratio, and the distance from a point to a line⁩

⁦If P divides AB in the ratio m : n (AP : PB = m : n), P is m(m + n) of the way from A to B⁩. ⁦Its coordinates are a weighted average of the two ends⁩: x = n·x١ + m·x٢m + n. ⁦Watch the order of the ratio⁩: ⁦1 : 2 means closer to A⁩.

⁦The shortest way from a point to a line is the perpendicular dropped from the point onto the line, not the vertical drop⁩. ⁦The length of that perpendicular is the distance from the point to the line⁩.

⁦For the line ax + by + c = ٠ and the point (x١,y١), the distance is d = |a·x١ + b·y١ + c|/√(a^٢ + b^٢)⁩.