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the equation of a diagonal line

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From Wikipedia

Diagonal

A diagonal is a line joining two nonconsecutive vertices of a polygon or polyhedron. Informally, any sloping line is called diagonal. The word "diagonal" derives from the Greekδιαγώνιος (diagonios), from dia- ("through", "across") and gonia ("angle", related to gony "knee"); it was used by both Strabo and Euclid to refer to a line connecting two vertices of a rhombus or cuboid,, and later adopted into Latin as diagonus ("slanting line").

In mathematics, in addition to its geometric meaning, a diagonal is also used in matrices to refer to a set of entries along a diagonal line.

Non-mathematical uses

In engineering, a diagonal brace is a beam used to brace a rectangular structure (such as scaffolding) to withstand strong forces pushing into it; although called a diagonal, due to practical considerations diagonal braces are often not connected to the corners of the rectangle.

Diagonal pliers are wire-cutting pliers whose cutting edges intersect the joint rivet at an angle or "on a diagonal".

A diagonal lashing is a type of lashing used to bind spars or poles together applied so that the lashings cross over the poles at an angle.

In association football, the diagonal system of control is the method referees and assistant referees use to position themselves in one of the four quadrants of the pitch.

Polygons

As applied to a polygon, a diagonal is a line segment joining any two non-consecutive vertices. Therefore, a quadrilateral has two diagonals, joining opposite pairs of vertices. For any convex polygon, all the diagonals are inside the polygon, but for re-entrant polygons, some diagonals are outside of the polygon.

Any n-sided polygon (n≥ 3), convex or concave, has

\frac{n^2-3n}{2}\,

diagonals, as each vertex has diagonals to all other vertices except itself and the two adjacent vertices, or n âˆ’ 3 diagonals.

Matrices

In the case of a square matrix, the main or principal diagonal is the diagonal line of entries running from the top-left corner to the bottom-right corner. For a matrix A with row index specified by i and column index specified by j, these would be entries A_{ij} with i = j. For example, the identity matrix can be defined as having entries of 1 on the main diagonal and zeroes elsewhere:

\begin{pmatrix}

1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}

The top-right to bottom-left diagonal is sometimes described as the minor diagonal or antidiagonal. The off-diagonal entries are those not on the main diagonal. A diagonal matrixis one whose off-diagonal entries are all zero.

A superdiagonal entry is one that is directly above and to the right of the main diagonal. Just as diagonal entries are those A_{ij} with j=i, the superdiagonal entries are those with j = i+1. For example, the non-zero entries of the following matrix all lie in the superdiagonal:

\begin{pmatrix}

0 & 2 & 0 \\ 0 & 0 & 3 \\ 0 & 0 & 0 \end{pmatrix} Likewise, a subdiagonal entry is one that is directly below and to the left of the main diagonal, that is, an entry A_{ij} with j = i - 1. General matrix diagonals can be specified by an index k measured relative to the main diagonal: the main diagonal has k = 0; the superdiagonal has k = 1; the subdiagonal has k = -1; and in general, the k-diagonal consists of the entries A_{ij} with j = i+k.

Geometry

By analogy, the subset of the Cartesian productX×X of any set X with itself, consisting of all pairs (x,x), is called the diagonal, and is the graph of the identity relation. This plays an important part in geometry; for example, the fixed points of a mappingF from X to itself may be obtained by intersecting the graph of F with the diagonal.

In geometric studies, the idea of intersecting the diagonal with itself is common, not directly, but by perturbing it within an equivalence class. This is related at a deep level with the Euler characteristic and the zeros of vector fields. For example, the circleS1 has Betti numbers 1, 1, 0, 0, 0, and therefore Euler characteristic 0. A geometric way of expressing this is to look at the diagonal on the two-torusS1xS1 and observe that it can move off itself by the small motion (θ, θ) to (θ, θ + ε). In general, the intersection number of the graph of a function with the diagonal may be computed using homology via the Lefschetz fixed point theorem; the self-intersection of the diagonal is the special case of the identity function.



From Yahoo Answers

Question:What type of lines have a slope of zero (vertical, horizontal, perpendicular, or diagonal?)

Answers:0 slope means that the line is parallel to x axis So it is horizontal. And has an equation as y =c If the line is vertical has a slope as undifined {c/0] or in minimum level of maths has a slope of infinity equatio : X =c For diagonal lines slope = 1 Y = x + c

Question:1. Indicate the equation of the given line in standard form. The line through (2, -1) and parallel to a line with slope of 3/4 2. Indicate the equation of the given line in standard form. The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2). 3. the equation of the given line in standard form. The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5). 4. Indicate in standard form the equation of the line passing through the given points. G(4, 6), H(1, 5) 5. Indicate the equation of the given line in standard form. The line through point (-3, 4) and perpendicular to a line that has slope 2/5 6. Indicate in standard form the equation of the line passing through the given point and having the given slope. E(3, 5), m = no slope 7. Indicate in standard form the equation of the line passing through the given point and having the given slope. D(5, -2) m = 2/5 8. Indicate in standard form the equation of the line passing through the given points. E(-2, 2), F(5, 1) 9. through the given points. R(3, 3), S(-6, -6) 10. Indicate the equation of the given line in standard form. The line containing the midpoints of the legs of right triangle ABC where A(-5, 5), B(1, 1), and C(3, 4) are the vertices. 11. Indicate in standard form the equation of the line passing through the given points. M(0, 6), N(6, 0) 12. Indicate in standard form the equation of the line passing through the given points. L(5, 0), M(0, 5) 13. Indicate in standard form the equation of the line passing through the given points. S(1/2, 1), T(1/2, 4) x = 1/2 y = 1/2 -2x + y = 0 14. Indicate in standard form the equation of the line passing through the given points. B(0, 0), C(4, -4) 15. Indicate the equation of the given line in standard form. The line containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0). 16. Indicate in standard form the equation of the line passing through the given point and having the given slope. A(5, 5), m = 3 17. Indicate the equation of the given line in standard form. The line containing the diagonal of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal. 18. Indicate in standard form the equation of the line passing through the given points. X(0, 6), Y(5, 6) 19. Indicate the equation of the given line in standard form. The line containing the longer diagonal of a quadrilateral whose vertices are A (2, 2), B(-2, -2), C(1, -1), and D(6, 4). 20. Indicate in standard form the equation of the line passing through the given point and having the given slope. B(6, 2), m = -1/2 21. Indicate in standard form the equation of the line passing through the given points. A(4, 1), B(5, 2) 22. Indicate the equation of the given line in standard form. The line with slope 9/7 and containing the midpoint of the segment whose endpoints are (2, -3) and (-6, 5). 23. Indicate in standard form the equation of the line passing through the given point and having the given slope. C(0, 4), m = 0 24. Indicate the equation of the given line in standard form. The line containing the hypotenuse of right triangle ABC where A(-5, 5), B(1, 1), and C(3, 4) are the vertices. 25. Indicate in standard form the equation of the line passing through the given points. P(6, 2), Q(8, -4)

Answers:25 questions about the same thing is a bit much don't you think? You have not shown any work! They are obviously just copied and pasted from your homework.

Question:A.all regular polygons B.no regular polygons C.regular polygons with an even number of sides D. regular polygons with an odd number of sides. ??????????? Dont answer if your going to fuss at me for needing HELP with my homework...........just give me an anwser.

Answers:C. Regular polygons with an even number of sides. Just try drawing a diagonal line of symmetry in a triangle or pentagon. Can't do it, can you? Now try it with a square or a hexagon... easy, right?

Question:?? please help like for a polygon with 4 sides there are 2 diagonals.. how many diagonals for a 50 sided polygon

Answers:Connect all points of a polygon with n sides, there're n(n-1)/2 line segments. There're n sides, so there're n(n-1)/2 - n = n(n-3)/2 diagonals. n = 50 => there're 50.47/2 = 1175 diagonals

From Youtube

Diagonal Lines :Explore how diagonal lines join two nonconsecutive vertices of a polygon.

3*3 Determinants Using Diagonals :demonstrations.wolfram.com The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. Copy the first two columns of the matrix to its right. Multiply along the blue lines and the red lines. Add the numbers on the bottom and subtract the numbers on the top. The result is the value of the determinant. Contributed by: George Beck