How to find the perimeter of the triangle defined by vertex coordinates

The perimeter is the length of the line bounding the occupied flat geometric figure of the square. For triangle, as well as all other polygon is a broken line, made up of his all sides. Therefore, the problem of computing the perimeter of a triangle, given the coordinates of its vertices, is reduced to calculating the length of each of the parties with subsequent summation of the obtained values.

How to find the perimeter of the triangle defined by vertex coordinates
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Instruction

To calculate the length of a side, consider the auxiliary the triangle made of the side and two of its projections on the axis of the abscissa and ordinate. In this figure two projections will form a right angle - it follows from the definition of rectangular coordinates. This means that they are sides in a right triangle, where the hypotenuse will be the side. Its length can be calculated by the Pythagorean theorem, we only need to find the length of the projections (of the legs). Each of the projections is a segment, the initial point which is defined in the lower coordinate end - greater, and their difference will be the length of the projection.

Calculate the length of each side. If the coordinates of the points defining the triangle as A(X₁,Y₁), B(X₂,Y₂) and C(X₃,Y₃), the side AB of the projection on the x-axis and the y will have a length X₂-X₁ and Y₂-Y₁, and the length of the side in accordance with the Pythagorean theorem will be equal to AB = √((X₂-X₁)2 + (Y₂-Y₁)2). The lengths of the other two sides, calculated via the projection on the coordinate axis, can be written as: VS = √(( X₃-X₂)2 + (Y₃-Y₂)2), CA = √((X₃-X₁)2 + (Y₃-Y₁)2).

When using a three-dimensional coordinate system in radical expression obtained in the previous step, add another term, which should Express the squared length of the projection side of the axis of the applicator that con. In this case, the coordinates of the points can be written as: A(X₁,Y₁,Z₁), B(X₂,Y₂,Z₂) and C(X₃,Y₃,Z₃). And the formulas for calculating the lengths of the sides will take the following form: AV = √((X₂-X₁)2 + (Y₂-Y₁)2 + (Z₂ - Z₁)2), VS = √(( X₃-X₂)2 + (Y₃-Y₂)2 + (Z₃-Z₂)2) and CA = √((X₃-X₁)2 + (Y₃-Y₁)2 + (Z₃ Is Z₁)2).

Calculate the perimeter (P) of a triangle, folded obtained in the previous steps, the lengths of the sides. For flat Cartesian coordinate system formula in a General form should look like this: P = AV + sun + SA = √((X₂-X₁)2 + (Y₂-Y₁)2) + √(( X₃-X₂)2 + (Y₃-Y₂)2) + √((X₃-X₁)2 + (Y₃-Y₁)2). For the three-dimensional coordinates, the same formula should look like this: R = √((X₂-X₁)2 + (Y₂-Y₁)2 + (Z₂ - Z₁)2) + √(( X₃-X₂)2 + (Y₃-Y₂)2 + (Z₃-Z₂)2) + √((X₃-X₁)2 + (Y₃-Y₁)2 + (Z₃ Is Z₁)2).

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