Sketch a model atleast 2 axioms of Pappus's Geometry and identify those axioms

Q: Three spheres, with radius R and lie in the same plane, are given such that each of the spheres…

A: Given, The radius of three sphere is From the given information we can draw the below diagram,

Q: Show that the triangle with vertices (5, 4, −1), (3, 6, −1), and (3, 4, 1) is equilateral.

A: To show that the triangle with vertices 5, 4, -1, 3, 6, -1 and 3, 4, 1 is equilateral. Solution: Let…

Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: Find the coordinates of vertices of a unit cube where the three concrrent edges are the coordinte…

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Q: Find the area of the hyperbolic (geodesic) triangle with vertices (3,0), (4,0) and (5,0).

A: Let P(3,0), Q(4,0) and R(5,0) be three vertices.  It is known that the equation of hyperbolic line…

Q: Create a set of 3 planes that intersect in a "Triangular Prism", as the picture shows. In other…

A: The equation of a plane is given by the formula ax+by+cz=d. The planes can be made depending upon…

Q: What is the image of the point (−5,−4) after a rotation of 180^{\circ}180∘ counterclockwise about…

A: Given The point is (-5 ,-4)  The rotate given point at 180 degree .

Q: 4. A point moves so that the sum of the squares of its distances from the faces of a cube is…

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Q: using projection concept, show thet ACで)-T。+ で

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Q: Find the points on the cone 22 + y? that are closest to the point (-2,2,0) %3D

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Q: For the three-point geometry, draw a pictorial representation different from those in our examples.…

A: Three point geometry is a finite geometry with the following four axioms: (a) There exist exactly…

Q: 3. Prove that points (5, 1), (2, -2), and (-1, –3) lie on a circle centred at (-2, 5). What is the…

A: Please rate and feel free to ask any query about any part.

Q: 7. Show that points (6, 1), (2, - 4), and (-2, 1) belong to an isoscles triangle.

A: 7. In this question we have to show that the given points belong to an isosceles triangle. Isosceles…

Q: An angle is in standard position if its vertex is at the ________ and its initial side isalong the…

A: An angle is in standard position if its vertex is at the ________ and its initial side is along the…

Q: . Prove that in a triangle, the orthocenter, centroid and the circumcenter are concurrent (in a…

A: Let X be the mid-point of EF Construct the median DX. Since G is the centroid, G is on DX by the…

Q: and B are vertices of the base of an isosceles triangle ABC. A is at point (1,2) and B at (4, -1).…

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Q: 13. Sketch an approximating graph for a triangle in the Euclidean plane, in Non-Euclidean plane, and…

A: Euclidean geometry refers to the general geometry of planes with no curvature. The curvature of the…

Q: 2. Locate point C such that mZDBC = mZBDC = mLADB. %3D %3D

A: I assume that You have already find the position of point D.

Q: Prove that the points 3,0),(4, 5),(-1, 4) and (-2,-1) taken in order, Lorm a rhombus, also find its…

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Q: Find point G on segment AB such that the ratio of AG to GB is 3:2

A: This is  a problem related to line and it's division. Based on the general formula and concept we…

Q: The vertices of quadrilateral KAIT are K(0,0), A(a, 0), I(a + b, c), and T(b, c). Use coordinate…

A: Parallelogram is a kind of quadrilateral with two pairs of opposite sides. In a parallelogram, the…

Q: A trapezoid has vertices located at the points: A(-2.3, 5), в(4.8, 5), с(4.8, —2.2), D(-2.3, –3.3).…

A: Use distance formula to find length            d=(x2-x1)2+(y2-y1)2

Q: Point K is on line segment JL. Given JL = x + 10, KL = 4x, and JK = 2x, determine the numerical…

A: The diagram according to the given information is shown below, so, the equation will be, JL=JK+KL…

Q: Depict the relationship of Parallel Postulate and Euclidean  Geometry.

A: Let's write answer,

Q: Specify in coordinates the projection made from point (1, 1) on the abscissa axis to the ordinate…

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Q: Which of the following isometric cube drawings demonstrates the result when a cube is added to each…

A: Given query is to find the the resultant figure when a cube is added to the shaded figure.

Q: A cubic polymom ial 3rd has 2, 3+i and one more. and what the origina the root what is is function.

A: Here, note that the complex root is always in a pair.

Q: 10 11 3 vertices at a parallelograni AaCD are shown in the appiet What are the coordinates of point…

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Q: (b) Determine the self-similarity dimension of the fractal.

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Q: 3. Use the distance formula to prove that the point (4,2) is on the parabola x = Sy. Prenared hu

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Q: Give 5 examples of radial symmetry in nature.

A: To give five exampleof Radial symmetry in nature.

Q: Show that the set of all points P that are twice as far from (-1,5,3) as from (6,2, –2) is a sphere.…

A: The set of all points P that are  twice as far from -1, 5, 3 as from 6, 2, -2. Let coordinate of a…

Q: Give an example of a tiling of the plane that has Regis symmetries but no symmetries of scale.

A: Solution: Rigid symmetry of pattern in the plane: It is motion of the plane that retains the pattern…

Q: Find all values of x so that the triangle with vertices A=(x, -3, 4), B=(-1,0, 6), and C=(-2, –2, 7)…

A: The given vertices are A=(x,-3,4), B=(-1,0,6) and C=(-2,-2,7) has area 4.

Q: Here is a regular hexagon. Draw in all lines of reflection symmetry

A: Draw a regular hexagon.

Q: The triangle with vertices A(0, 1, 2), B(-1,0,2) and C(1,-2,0) has area = (ii)

A: A(0,1,2) B(-1,0,2) C(1,-2,0)

Q: Plot the quadrilateral after being rotated 180°. Label the vertices of the image. L St -М

A: Basic coordinate geometry problem

Q: Draw three shapes that are symmetric. Draw at least one line of symmetry through each shape to prove…

A: The symmetric shape's are given below

Q: 2 Point P is equidistant from both [AB] and [AC]. Use congruence to show that P lies on the bisector…

A: Point P is equidistant from both AB and AC. By using congruence to show that P lies on the bisector…

Q: 13. . There are 8 points in a plane out of which 3 are collinear. How many straight lines can be…

A: There are 8 points in a plane out of which 3 are collinear and 5 are non collinear points.

Q: Based on triangulation of polygons, prove that copies of a regular n- gon can tile the plane only…

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Q: In the geometry of Desargues, which axiom is not true statement in Euclidean geometry? * Axiom1…

A: There are six axioms in the geometry of Desargues as follow: Axiom 1) There exists as least one…

Q: Find all values of x so that the triangle with vertices A=(-2, –1, x), B=(-4, -2, –2), and C=(-2,…

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Q: Point P is on segment AB such that AP:PB is 4:5. If A has coordinates (4,2), and B has coordinates…

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Q: In quadrilateral RSTV, the midpoints of consecutive sides are joined in order. Try drawing other…

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Q: An integer point is a point on the xy-plane with both coordinates integer. Given a convex pentagon…

A: Hint:  using the concept of convex

Q: 9. Under what conditions could a geometry satisfy more than one of the parallel postulates? Explain.…

A: There are some points with explanation and example to understand you better.

Q: Show that the quadrilateral having vertices at (1, 1,3), (-2,1,-1), (-5,4, 0), and (-8, 4,-4) is a…

A: This is a problem related to area of the parallelogram by cross products. Based on the general…

Q: Show that the points form the vertices of the polygon. right triangle: (−4, 5), (0, 7), (2, 3)…

A: The given points are -4,5, 0,7, 2,3

Q: A trapezoid is a quadrilateral with at least one pair of parallel sides. Show that the quadrilateral…

A: slope of the line joining (x1,y1),(x2,y2)  is y2-y1x2-x1