Mathematical tables: typical analytic geometry related formulas
Tables show typical formulas related to analytic geometry such as distance between two points.

Beta version#

BETA TEST VERSION OF THIS ITEM
This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
Feel free to send any ideas and comments !

Line segment#

 Name Formula Legend Distance between two points (line segment length) Show source$|AB|=\sqrt{\left(B_x-A_x\right)^{2}+\left(B_y-A_y\right)^{2}}$ $|AB|$ - the distance between points (the length of the segment beginning at point A and ending at point B),$A_x$, $A_y$ - coordinates of the first point,$B_x$, $B_y$ - coordinates of the second point. The midpoint of the line segment: x-coordinate Show source$C_x=\frac{A_x+B_x}{2}$ $C_x$ - the x-coordinate of the midpoint,$A_x$ - x-coordinate of the first point,$B_x$ - x-coordinate of the second point. The midpoint of the line segment: y-coordinate Show source$C_y=\frac{A_y+B_y}{2}$ $C_y$ - the y-coordinate of the midpoint,$A_y$ - y-coordinate of the first point,$B_y$ - y-coordinate of the second point.

Line segment in three-dimensional space#

 Name Formula Legend Distance between two points in three-dimensional space (line segment length) Show source$|AB|=\sqrt{\left(B_x-A_x\right)^{2}+\left(B_y-A_y\right)^{2}+\left(B_z-A_z\right)^{2}}$ $|AB|$ - the distance between points (the length of the segment beginning at point A and ending at point B),$A_x$, $A_y$, $A_z$ - coordinates of the first point,$B_x$, $B_y$, $B_z$ - coordinates of the second point. The midpoint of the line segment in three-dimensional space: x-coordinate Show source$C_x=\frac{A_x+B_x}{2}$ $C_x$ - the x-coordinate of the midpoint,$A_x$ - x-coordinate of the first point,$B_x$ - x-coordinate of the second point. The midpoint of the line segment in three-dimensional space: y-coordinate Show source$C_y=\frac{A_y+B_y}{2}$ $C_y$ - the y-coordinate of the midpoint,$A_y$ - y-coordinate of the first point,$B_y$ - y-coordinate of the second point. The midpoint of the line segment in three-dimensional space: z-coordinate Show source$C_z=\frac{A_z+B_z}{2}$ $C_z$ - the z-coordinate of the midpoint,$A_z$ - z-coordinate of the first point,$B_z$ - z-coordinate of the second point.

Symmetry with respect to the x-axis#

 Name Formula Legend The symmetric point in respect to the x-axis: x coordinate Show source$x^{\prime}=-x$ $x^{\prime}$ - the x-coordinate of the point image,$x$ - x-coordinate of the original point. The symmetric point in respect to the x-axis: y coordinate Show source$y^{\prime}=y$ $y^{\prime}$ - the y-coordinate of the point image,$y$ - y-coordinate of the original point.

Symmetry with respect to the y-axis#

 Name Formula Legend The symmetric point in respect to the y-axis: x coordinate Show source$x^{\prime}=x$ $x^{\prime}$ - the x-coordinate of the point image,$x$ - x-coordinate of the original point. The symmetric point in respect to the y-axis: y coordinate Show source$y^{\prime}=-y$ $y^{\prime}$ - the y-coordinate of the point image,$y$ - y-coordinate of the original point.

Symmetry with the respect to the origin#

 Name Formula Legend The symmetric point in respect to the origin: x coordinate Show source$x^{\prime}=-x$ $x^{\prime}$ - the x-coordinate of the point image,$x$ - x-coordinate of the original point. The symmetric point in respect to the origin: y coordinate Show source$y^{\prime}=-y$ $y^{\prime}$ - the y-coordinate of the point image,$y$ - y-coordinate of the original point.

2D translation (two-dimensional space)#

 Name Formula Legend Translate point by vector: x coordinate Show source$x^{\prime}=x+V_x$ $x^{\prime}$ - the x-coordinate of the point image,$x$ - x-coordinate of the original point,$V_x$ - the x-coordinate of the vector. Translate point by vector: y coordinate Show source$y^{\prime}=y+V_y$ $y^{\prime}$ - the y-coordinate of the point image,$y$ - y-coordinate of the original point,$V_y$ - the y-coordinate of the vector.

3D translation (three-dimensional space)#

 Name Formula Legend Translate point by vector: x coordinate Show source$x^{\prime}=x+V_x$ $x^{\prime}$ - the x-coordinate of the point image,$x$ - x-coordinate of the original point,$V_x$ - the x-coordinate of the vector. Translate point by vector: y coordinate Show source$y^{\prime}=y+V_y$ $y^{\prime}$ - the y-coordinate of the point image,$y$ - y-coordinate of the original point,$V_y$ - the y-coordinate of the vector. Translate point by vector: z coordinate Show source$z^{\prime}=z+V_z$ $z^{\prime}$ - the z-coordinate of the point image,$z$ - z-coordinate of the original point,$V_z$ - the z-coordinate of the vector.

2D rotation (two-dimensional space)#

 Name Formula Legend Rotate point around z-axis: x coordinate Show source$x^{\prime}=x \cdot cos\left(\theta\right)-y \cdot sin\left(\theta\right)$ $x^{\prime}$ - the x-coordinate of the point image,$x$ - x-coordinate of the original point,$y$ - y-coordinate of the original point,$\theta$ - rotation angle. Rotate point around z-axis: y coordinate Show source$y^{\prime}=x \cdot sin\left(\theta\right)+y \cdot cos\left(\theta\right)$ $y^{\prime}$ - the y-coordinate of the point image,$x$ - x-coordinate of the original point,$y$ - y-coordinate of the original point,$\theta$ - rotation angle.

3D rotation around z-axis#

 Name Formula Legend Rotate point around z-axis: x coordinate Show source$x^{\prime}=x \cdot cos\left(\theta\right)-y \cdot sin\left(\theta\right)$ $x^{\prime}$ - the x-coordinate of the point image,$x$ - x-coordinate of the original point,$y$ - y-coordinate of the original point,$\theta$ - rotation angle. Rotate point around z-axis: y coordinate Show source$y^{\prime}=x \cdot sin\left(\theta\right)+y \cdot cos\left(\theta\right)$ $y^{\prime}$ - the y-coordinate of the point image,$x$ - x-coordinate of the original point,$y$ - y-coordinate of the original point,$\theta$ - rotation angle. Rotate point around z-axis: z coordinate Show source$z^{\prime}=z$ $z^{\prime}$ - the z-coordinate of the point image,$z$ - z-coordinate of the original point.

3D rotation around x-axis#

 Name Formula Legend Rotate point around x-axis: x coordinate Show source$x^{\prime}=x$ $x^{\prime}$ - the x-coordinate of the point image,$x$ - x-coordinate of the original point. Rotate point around x-axis: y coordinate Show source$y^{\prime}=y \cdot cos\left(\theta\right)-z \cdot sin\left(\theta\right)$ $y^{\prime}$ - the y-coordinate of the point image,$y$ - y-coordinate of the original point,$z$ - z-coordinate of the original point,$\theta$ - rotation angle. Rotate point around x-axis: z coordinate Show source$z^{\prime}=z \cdot cos\left(\theta\right)+y \cdot sin\left(\theta\right)$ $z^{\prime}$ - the z-coordinate of the point image,$z$ - z-coordinate of the original point,$y$ - y-coordinate of the original point,$\theta$ - rotation angle.

3D rotation around y-axis#

 Name Formula Legend Rotate point around y-axis: x coordinate Show source$x^{\prime}=x \cdot cos\left(\theta\right)-z \cdot sin\left(\theta\right)$ $x^{\prime}$ - the x-coordinate of the point image,$x$ - x-coordinate of the original point,$z$ - z-coordinate of the original point,$\theta$ - rotation angle. Rotate point around y-axis: y coordinate Show source$y^{\prime}=y$ $y^{\prime}$ - the y-coordinate of the point image,$y$ - y-coordinate of the original point. Rotate point around y-axis: z coordinate Show source$z^{\prime}=z \cdot cos\left(\theta\right)+x \cdot sin\left(\theta\right)$ $z^{\prime}$ - the z-coordinate of the point image,$z$ - z-coordinate of the original point,$x$ - x-coordinate of the original point,$\theta$ - rotation angle.

Some facts#

• Analytic geometry is a branch of mathematics that deals with the study of geometrical shapes by the analytical and algebraic methods.
• Analytical geometry is a bridge between classical geometry and algebra.
• Analytical geometry methods allow you to replace the problems known from classical geometry for equivalent problems known from algebra, e.g. into a system of equations.
• If you're looking for calculator that takes the classic Euclidean geometry into account, check our other calculator: Math tables: geometry.

Links to external sites (leaving Calculla?)#

JavaScript failed !
So this is static version of this website.
This website works a lot better in JavaScript enabled browser.