What is Coordinate geometry: Definition and 56 Discussions

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry.
Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space (three dimensions). As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.

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    What is the Method for Finding Points Inside a Triangle Using Inequalities?

    Coordinate Geometry II HARD! 1a). TriangleABC has vertices A(4,6), B(-3,4) and C(-1,-3). Write down the three inequalities whose intersection is the interior of triangleABC. 1b). Prove that triangleABC is a right angled isosceles triangle. 2a). The lines L1 and L2 have the equations...
  2. R

    Coordinate Geometry: Point Division in Ratio 2 : 5

    Hi i'm stuck on this question . please could someone guide me in the right direction ? A = (1, - 2,4) and B = (8,12, - 3). Find the co-ordinates of the point which divides AB in the ratio 2 : 5. thanx roger
  3. U

    Arghhh Coordinate geometry question

    Hi everyone. This is a question that was attempted in class but no on (including our teacher) could solve in the time we had left. It's not actually homework, but it's really getting on my nerves! The quadrilateral ABCD, where A is (4,5) and C is (3, -2), is a square. Find the coordinates of...
  4. G

    Coordinate geometry - circles.

    I'm just introducing myself to coordinate geometry in the xy plane of cirlces. Here's a question I'm having trouble with: Q11: The line with equation y=mx is a tangent to the circle with equation x^2 + y^2 - 6x - 6y + 17 = 0. Find the possible values of m. At first i thought i'd try...
  5. denian

    Solve Rhombus: Coordinate Geometry Question

    just want to ask a simple question a quadrilateral has the vertices A ( 1,4 ), B (9,5 ) , C ( 5,-2) and D (-3,-3). show that the quadrilateral is a rhombus what i do is find gradient AB, CD, AD and BC. and then state which and which have the same gradient... and hence the opposite sides...
  6. denian

    Coordinate Geometry: Triangle Vertices & Point P Movement in OAB Plane

    the vertices of a triangle are 0, and the points A (a, 0) and B (0,a) where a>0. the point P moves in the plane OAB such that OP square + AP square + BP square = k square, where k is a positive constant. show that k mst be bigger than (2/3)a X square root of 3 i tried. but can't even know...
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