Summary
1. The distance between $P(x_1, y_1)$ and $Q(x_2, y_2)$ is $√{(x_2-x_1)^2+(y_2-y_1)^2}$ 2. The distance of a point $P(x, y)$ from the origin is $√{x^2+y^2}$ 3. The coordinates of the point $P(x, y)$ which divides the line segment joining the points A$(x_1, y_1)$ and B$(x_2, y_2)$ internally in the ratio $m_1 : m_2$ are $({m_1 x_2 + m_2 x_1}/{m_1 + m_2},{m_1 y_2 + m_2 y_1}/{m_1 + m_2})$ 4. The mid-point of the line segment joining the points $P(x_1, y_1)$ and $Q(x_2, y_2)$ is ${x_1+x_2}/2,{y_1+y_2}/2$ 5. The area of the triangle formed by the points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ is the numerical value of the expression ${1/2}{[x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 – y_2)]}$