coordinate geometry

The distance between P(x1, y1) and Q(x2, y2) is

= √ (X2 - X1)² + ( Y2 - Y1)²

The distance of a point P(x, y) from the origin is

= √ X² + Y²

The coordinates of the point P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2, y2) internally in the ratio m1 : m2 are

$$ \left( \frac{m_1 x_2 + m_2 x_1}{m_1 + m_2}, \frac{m_1 y_2 + m_2 y_1}{m_1 + m_2} \right) $$

The Mid-Point of the line segment joining the points P(x1, y1) and Q(x2, y2) is

$$ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) $$