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 !
⌛ Loading...

Line segment#

NameFormulaLegend
Distance between two points (line segment length)Show sourceAB=(BxAx)2+(ByAy)2|AB|=\sqrt{\left(B_x-A_x\right)^{2}+\left(B_y-A_y\right)^{2}}
  • AB|AB| - the distance between points (the length of the segment beginning at point A and ending at point B),
  • AxA_x, AyA_y - coordinates of the first point,
  • BxB_x, ByB_y - coordinates of the second point.
The midpoint of the line segment: x-coordinateShow sourceCx=Ax+Bx2C_x=\frac{A_x+B_x}{2}
  • CxC_x - the x-coordinate of the midpoint,
  • AxA_x - x-coordinate of the first point,
  • BxB_x - x-coordinate of the second point.
The midpoint of the line segment: y-coordinateShow sourceCy=Ay+By2C_y=\frac{A_y+B_y}{2}
  • CyC_y - the y-coordinate of the midpoint,
  • AyA_y - y-coordinate of the first point,
  • ByB_y - y-coordinate of the second point.

Line segment in three-dimensional space#

NameFormulaLegend
Distance between two points in three-dimensional space (line segment length)Show sourceAB=(BxAx)2+(ByAy)2+(BzAz)2|AB|=\sqrt{\left(B_x-A_x\right)^{2}+\left(B_y-A_y\right)^{2}+\left(B_z-A_z\right)^{2}}
  • AB|AB| - the distance between points (the length of the segment beginning at point A and ending at point B),
  • AxA_x, AyA_y, AzA_z - coordinates of the first point,
  • BxB_x, ByB_y, BzB_z - coordinates of the second point.
The midpoint of the line segment in three-dimensional space: x-coordinateShow sourceCx=Ax+Bx2C_x=\frac{A_x+B_x}{2}
  • CxC_x - the x-coordinate of the midpoint,
  • AxA_x - x-coordinate of the first point,
  • BxB_x - x-coordinate of the second point.
The midpoint of the line segment in three-dimensional space: y-coordinateShow sourceCy=Ay+By2C_y=\frac{A_y+B_y}{2}
  • CyC_y - the y-coordinate of the midpoint,
  • AyA_y - y-coordinate of the first point,
  • ByB_y - y-coordinate of the second point.
The midpoint of the line segment in three-dimensional space: z-coordinateShow sourceCz=Az+Bz2C_z=\frac{A_z+B_z}{2}
  • CzC_z - the z-coordinate of the midpoint,
  • AzA_z - z-coordinate of the first point,
  • BzB_z - z-coordinate of the second point.

Symmetry with respect to the x-axis#

NameFormulaLegend
The symmetric point in respect to the x-axis: x coordinateShow sourcex=xx^{\prime}=-x
  • xx^{\prime} - the x-coordinate of the point image,
  • xx - x-coordinate of the original point.
The symmetric point in respect to the x-axis: y coordinateShow sourcey=yy^{\prime}=y
  • yy^{\prime} - the y-coordinate of the point image,
  • yy - y-coordinate of the original point.

Symmetry with respect to the y-axis#

NameFormulaLegend
The symmetric point in respect to the y-axis: x coordinateShow sourcex=xx^{\prime}=x
  • xx^{\prime} - the x-coordinate of the point image,
  • xx - x-coordinate of the original point.
The symmetric point in respect to the y-axis: y coordinateShow sourcey=yy^{\prime}=-y
  • yy^{\prime} - the y-coordinate of the point image,
  • yy - y-coordinate of the original point.

Symmetry with the respect to the origin#

NameFormulaLegend
The symmetric point in respect to the origin: x coordinateShow sourcex=xx^{\prime}=-x
  • xx^{\prime} - the x-coordinate of the point image,
  • xx - x-coordinate of the original point.
The symmetric point in respect to the origin: y coordinateShow sourcey=yy^{\prime}=-y
  • yy^{\prime} - the y-coordinate of the point image,
  • yy - y-coordinate of the original point.

2D translation (two-dimensional space)#

NameFormulaLegend
Translate point by vector: x coordinateShow sourcex=x+Vxx^{\prime}=x+V_x
  • xx^{\prime} - the x-coordinate of the point image,
  • xx - x-coordinate of the original point,
  • VxV_x - the x-coordinate of the vector.
Translate point by vector: y coordinateShow sourcey=y+Vyy^{\prime}=y+V_y
  • yy^{\prime} - the y-coordinate of the point image,
  • yy - y-coordinate of the original point,
  • VyV_y - the y-coordinate of the vector.

3D translation (three-dimensional space)#

NameFormulaLegend
Translate point by vector: x coordinateShow sourcex=x+Vxx^{\prime}=x+V_x
  • xx^{\prime} - the x-coordinate of the point image,
  • xx - x-coordinate of the original point,
  • VxV_x - the x-coordinate of the vector.
Translate point by vector: y coordinateShow sourcey=y+Vyy^{\prime}=y+V_y
  • yy^{\prime} - the y-coordinate of the point image,
  • yy - y-coordinate of the original point,
  • VyV_y - the y-coordinate of the vector.
Translate point by vector: z coordinateShow sourcez=z+Vzz^{\prime}=z+V_z
  • zz^{\prime} - the z-coordinate of the point image,
  • zz - z-coordinate of the original point,
  • VzV_z - the z-coordinate of the vector.

2D rotation (two-dimensional space)#

NameFormulaLegend
Rotate point around z-axis: x coordinateShow sourcex=xcos(θ)ysin(θ)x^{\prime}=x \cdot cos\left(\theta\right)-y \cdot sin\left(\theta\right)
  • xx^{\prime} - the x-coordinate of the point image,
  • xx - x-coordinate of the original point,
  • yy - y-coordinate of the original point,
  • θ\theta - rotation angle.
Rotate point around z-axis: y coordinateShow sourcey=xsin(θ)+ycos(θ)y^{\prime}=x \cdot sin\left(\theta\right)+y \cdot cos\left(\theta\right)
  • yy^{\prime} - the y-coordinate of the point image,
  • xx - x-coordinate of the original point,
  • yy - y-coordinate of the original point,
  • θ\theta - rotation angle.

3D rotation around z-axis#

NameFormulaLegend
Rotate point around z-axis: x coordinateShow sourcex=xcos(θ)ysin(θ)x^{\prime}=x \cdot cos\left(\theta\right)-y \cdot sin\left(\theta\right)
  • xx^{\prime} - the x-coordinate of the point image,
  • xx - x-coordinate of the original point,
  • yy - y-coordinate of the original point,
  • θ\theta - rotation angle.
Rotate point around z-axis: y coordinateShow sourcey=xsin(θ)+ycos(θ)y^{\prime}=x \cdot sin\left(\theta\right)+y \cdot cos\left(\theta\right)
  • yy^{\prime} - the y-coordinate of the point image,
  • xx - x-coordinate of the original point,
  • yy - y-coordinate of the original point,
  • θ\theta - rotation angle.
Rotate point around z-axis: z coordinateShow sourcez=zz^{\prime}=z
  • zz^{\prime} - the z-coordinate of the point image,
  • zz - z-coordinate of the original point.

3D rotation around x-axis#

NameFormulaLegend
Rotate point around x-axis: x coordinateShow sourcex=xx^{\prime}=x
  • xx^{\prime} - the x-coordinate of the point image,
  • xx - x-coordinate of the original point.
Rotate point around x-axis: y coordinateShow sourcey=ycos(θ)zsin(θ)y^{\prime}=y \cdot cos\left(\theta\right)-z \cdot sin\left(\theta\right)
  • yy^{\prime} - the y-coordinate of the point image,
  • yy - y-coordinate of the original point,
  • zz - z-coordinate of the original point,
  • θ\theta - rotation angle.
Rotate point around x-axis: z coordinateShow sourcez=zcos(θ)+ysin(θ)z^{\prime}=z \cdot cos\left(\theta\right)+y \cdot sin\left(\theta\right)
  • zz^{\prime} - the z-coordinate of the point image,
  • zz - z-coordinate of the original point,
  • yy - y-coordinate of the original point,
  • θ\theta - rotation angle.

3D rotation around y-axis#

NameFormulaLegend
Rotate point around y-axis: x coordinateShow sourcex=xcos(θ)zsin(θ)x^{\prime}=x \cdot cos\left(\theta\right)-z \cdot sin\left(\theta\right)
  • xx^{\prime} - the x-coordinate of the point image,
  • xx - x-coordinate of the original point,
  • zz - z-coordinate of the original point,
  • θ\theta - rotation angle.
Rotate point around y-axis: y coordinateShow sourcey=yy^{\prime}=y
  • yy^{\prime} - the y-coordinate of the point image,
  • yy - y-coordinate of the original point.
Rotate point around y-axis: z coordinateShow sourcez=zcos(θ)+xsin(θ)z^{\prime}=z \cdot cos\left(\theta\right)+x \cdot sin\left(\theta\right)
  • zz^{\prime} - the z-coordinate of the point image,
  • zz - z-coordinate of the original point,
  • xx - x-coordinate of the original point,
  • θ\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.

Tags and links to this website#

What tags this calculator has#

Permalink#

This is permalink. Permalink is the link containing your input data. Just copy it and share your work with friends:

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.
Please enable JavaScript.