Learning these TS Inter 1st Year Maths 1B Formulas Chapter 5 Three Dimensional Coordinates will help students to solve mathematical problems quickly.

## TS Inter 1st Year Maths 1B Three Dimensional Coordinates Formulas

→ Perpendicular distances front the point P(x, y, z ) to yz, zx and xy planes are |x|, |y|, |z|.

→ The distance between points A (x_{1}, y_{1}, z_{1}), B (x_{2}, y_{2}, z_{2}) is AB = \(\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2+\left(z_1-z_2\right)^2}\)

→ The coordinates of a point which divides A = (x_{1}, y_{1}, z_{1}) and B = (x_{2}, y_{2}, z_{2}) internally in the ratio m_{1} m_{2} is = \(\left(\frac{m_1 x_2+m_2 x_1}{m_1+m_2}, \frac{m_1 y_2+m_2 y_1}{m_1+m_2}, \frac{m_1 z_2+m_2 z_1}{m_1+m_2}\right)\)

→ Coordinates of midpoint of a line segment AB joining

A = (x_{1}, y_{1}, z_{1}) and B = (x_{2}, y_{2}, z_{2}) is = \(\left(\frac{\mathrm{x}_1+\mathrm{x}_2}{2}, \frac{\mathrm{y}_1+\mathrm{y}_2}{2}, \frac{\mathrm{z}_1+\mathrm{z}_2}{2}\right)\).

→ The centroid of the triangle formed by the points A (x_{1}, y_{1}, z_{1}) , B (x_{2}, y_{2}, z_{2}), C(x_{3}, y_{3}, z_{3}) is

G = \(\left(\frac{\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3}{3}, \frac{\mathrm{y}_1+\mathrm{y}_2+\mathrm{y}_3}{3}, \frac{\mathrm{z}_1+\mathrm{z}_2+\mathrm{z}_3}{3}\right)\)

→ The centroid of the tetrahedron formed by (x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2}), (x_{3}, y_{3}, z_{3}) and (x_{4}, y_{4}, z_{4}) is

G = \(\left(\frac{x_1+x_2+x_3+x_4}{4}, \frac{y_1+y_2+y_3+y_4}{4}, \frac{z_1+z_2+z_3+z_4}{4}\right)\)