1. Consider the finite projective Geometry satisfying the well-known axioms A1-A6 and having two Lines L and L'. If L contains exactly n points, while L' UL contains exactly 9 points. Then n = A) 9 B) 5 C) 73 D) 10 E) N.A.

Q: 9. DABCD is a convex quadrilateral. Let P, Q, R, S be centers of the squares drawn (externally to…

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Q: A(n)................................... is the collection of all points in the plane such that the…

A: We know, A parabola is a collection of all the points in a plane such that the distance from each…

Q: 2. Prove that if two straight line segments r and r'are parallel transports another straight line L,…

A: Consider the equation

Q: Prove the following theorem in neutral geometry: If there exists a constant c and a model for…

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Q: Prove that quadrilateral PLUS with the vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle.…

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Q: Prove that the are length af Curve y = leg secx from N =0 to 3 is leg ta+ 45) .

A: The formula of arc length is given below:

Q: . In any projective plane, there are at least 4 points not lying on a given line.

A: False.  Correct Statement is: In any projective plane there at least 3 points lying on a given line.…

Q: 12) Show that D. ldi-del is shortest distance bet uleen ax-by+c2di i and ax+by tcz =dz?

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Q: Prove that if A-C-D, B-F-C, and A-F-G (all in the same plane) and A, B, and C are noncollinear, then…

A: Given:  ACD , BFC and AFG all are in same plane and A,B and C are noncollinear , then G is the…

Q: 4. Given that lines PQ and RS are parallel and t is a transversal, use a two column proof to prove…

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Q: 3. Decide whether the following statement is TRUE or FALSE. If TRUE, give a short explanation. If…

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Q: Prove a quadrilateral with vertices G(1,1), H(5,3), I(4,5) and J(0,3) is a rectangle

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Q: let ABCD be a reactangle.The perpendicular bisector of line segment BD intersects line AB and BC in…

A: In this rectangle ABCD the perpendicular bisector of diagonal BD is EF and EF will be AC.

Q: Consider an incidence geometry satisfying the betweenness axioms. Let A,B,C be points on a line /…

A: Given ta is parallel to tb and tb is parallel to tc

Q: 5. If r = (r, (x, y, z) and ro = (xo, Yo, 20), describe precisely the set of all points (r, y, z)…

A: We plug the given values in the given equation and simplify

Q: 1. If C₁ is the segment from (x₁, y₁) to (x2, y2), find Ja x dy - y dx in terms of the four…

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Q: Show that the closed interval [0, 1] and the unit circle S' = {(x, y)|x² + y² = 1} cannot be…

A: Suppose there exist a homeomorphism f:[0, ∞)----->R then restriction of f f|[0,∞)\{0} : [0,…

Q: Given: Rhombus ABCD with diagonals AC and BD intersecting at point E Complete the table to prove…

A: The rhombus is a quadrilateral with all sides equal in length. The diagonals of a rhombus are angles…

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: Let ABCD be a rectangle. The perpendicular bisector of line segment BD intersects lines AB and BC in…

A: Draw the diagram as shown below : Calculate the cordinates of L .L=a+02,b+02=a2,b2Calculate of…

Q: In an Argand plane, a O straight line O point O circle

A: The given complex number is z=16 z=16x+iy=16+i0

Q: Prove: In Fano’s Geometry, show that for a set of three lines not all containing the same point,…

A: Axioms3 of Fano’s geometry: The axiom 3 in Fano’s geometry is stated as “not all points of the…

Q: Find an eguaton for the set of all points (a sy, z) equiditant fom point (1,0,2) and

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Q: perpendicular to AB, and in traingle XYZ, lines ZW is perpendicular to XY.      If AB = XY and CD =…

A: Given query is to find the correct option for the triangle.

Q: IfL is a line through 0 and if ŷ is the orthogonal projection of y onto L, then || ŷ||l gives the…

A: The given statement is "If L is a line through 0 and if y^ is the orthogonal projection of y onto L,…

Q: a subipace of Masa And, the set s-{(:),(;:), () #) w {():x, YaR} i) W = {Ğ ): x, Question 3 -{:9),(?…

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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: which axioms for a finite projective plane are also valid in Euclidean geometry? which are not?

A: A finite geometry is any geometric system that has only a finite number of points. The familiar…

Q: 3) Consider the line L in R? spanned byp = (6). Let PL(u) be the orthogonal %3D projection of the u…

A: b = 4

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: Prove that all the points on a perpendicular bisector of a line segment AB are equidistant from the…

A: Statement:All the points on a perpendicular bisector of a line segment AB are equidistant from the…

Q: 2 Prove that a quadrilateral with the vertices A(-2,3), B(2,6), C(7,6) and D(3,3) is a rhombus. IB

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Q: Suppose that four lines in a given plane a1, a2, b1. bz are given, with the conditions (also given)…

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Q: Prove that a circle in H projects to a Euclidean circle in D. Conclude that not all triangles in…

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Q: show that the points ACI,I,4), B(2,2,2), c (o,1,5) and D(1,0,5) coplanear (in the ave Same plane).

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Q: Let ABCD be a rectangle. The perpendicular bisector of line segment BD intersects lines AB and BC in…

A: We need to prove FM and EN are perpendicular.

Q: 1) Prove that T = { diag ( eia eip, eilxip)) | a,B E [0,27()} ís maximal torus in sul 3).

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Q: 2.) Example: Prove the Symmetric Property for the line segments. Given: PQ XY Prove: XY PQ P. Y Q

A: For the given line segments PQ≅XY

Q: Prove Green's theorem for the rectangle defined by xo < x < x1 Yo < y < Y1 (a) directly, and (b)…

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Q: Find a geometric model for the following axioms, and determine whether or not it is a projective…

A: Yes, it is possible... If you carefully observe, you will see that this should give us a pentagon,…

Q: What point divides the directed line segment AB into a 2:3 4. ratio? 3- -2- 456 89 10 11 12 13 14 15…

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Q: - Consider noncoplanar points A, B, C, and D. Using three points at a time (such as A, B, and C),…

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Q: 7. Let ABCD be a parallelogram in the affine plane. Prove that the line connecting the midpoints of…

A: Given that, Let ABCD be a parallelogram in the affine plane. Prove that the line connecting the…

Q: If there are 9 distinct points on a plane, no 3 of which are collinear, how many quadrilaterals can…

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Q: 14 14 Assume that SV is the perpendicular bisector of RT. If VR is congruent to VT, what is the…

A: SV↔ is the perpendicular bisector of RT¯.VR¯ is congruent to VT¯we have to find the length of SR¯

Q: Show that the points E(2, 2, 2), F(2, 0, 1), G(4, 1, -1) and H(4, 3, 0) are coplanar and that they…

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Q: It is about proofs.

A: Draw a circle. Let AB is the diameter. AC and BD are two chords from the ends of the diameter so…

Q: In init square ABCD, the inscribed circle w intersects CD at M and AM intersects w at a point P…

A: The figure of the given situation:  ABCD is unit square.  w is an inscribed circle of radius 0.5 and…

Q: 7. What additional piece is needed to prove JMLK is a rhombus ?

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Q: (a) is the pazint (2,-2, 1s The point (2, I, 5) on the ime? explain ) fiad he paint where the line…

A: This is a problem of 3D geometry and parametric forms of straight lines in 3D.