Given parallelogram ABCD with vertices A(-3,1), B (2,6), C(9,5) and D(4,0) PROVE ABCD is a rhombus.

Q: The parallelogram (ABCD) has vertices at A(2,-1,4), B(1,0, –1), C(1, 2, 3), and D, then اخترأحد…

A: We have to find Coordinate D, Area of parallelogram and projection of BC onto BA.

Q: The vertices of quadrilateral JOHN are J(-3,1), O(3,3), H(5,7), and N(-1,5). Use coordinate geometry…

A: We are given the vertices J(-3, 1), O(3, 3), H(5, 7), and N(-1, 5). Let us plot the graph first.

Q: Given: AABC with vertices A(-6,-2), B(2,8), and C(6,-2). AB has midpoint D, BC has midpoint E, and…

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Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(8, 7,…

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Q: Show that the diagonals of a parallelogram are perpendicular if and only if it is a rhombus, i.e.,…

A: please find the attached solution

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(8, -2,…

A: FIND THE AREA

Q: 3. ABCD is a rhombus; find the following:

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Q: The parallelogram (ABCD) has vertices at A(2, -1, 4), B(1,0,-1), C(1,2,3), and D, then اخترأحد…

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Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(-1, 6,…

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Q: A quadrilateral has vertices Q (-2, -2), R (0, 2), S (4, 3), and T (3,-1). Which statement about…

A: Solution: The objective is to determine the statement about quadrilateral QRST

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(-2, -6,…

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Q: Let points A; B , C , and D in R3 have respective coordinates (1, 2, 3), (−2, 3, 5), (0, 3, 6), and…

A: Given: A(1, 2, 3), B(−2, 3, 5), C(0, 3, 6), D(3, 2, 4)

Q: A(-3, 2), В(5, — 4), С(7, 7)

A: Consider the given points,  Now, prove that C is on the perpendicular bisector of segment…

Q: 1. The vertices of quadrilateral ABCD are A(-2,3), B(4,6), C(10,3), and D(0,-2). Use coordinate…

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Q: 1. Rhombus ABCD with vertices A(-3, -2), B(0, 3), C(5, 6), and D(2, 1): (x, y)- (x+2, y-6)

A: In Rhombus, A=(-3,-2)B=(0,3)C=(5,6)D=(2,1)

Q: The parallelogram (ABCD) has vertices at A(2,-1, 4), B(1,0, -1).C(1,2,3), and D, then

A: Let A(2,-1,4) , B(1,0,-1) , C( 1,2,3) and D(x,y,z) Let AC be one diagonal and BD be another…

Q: The parallelogram (ABCD) has vertices at A(2,-1, 4), B(1,0,-1), C(1,2, 3), and D, then اخترأحد…

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Q: If EF is the perpendicular bisector of CD, find x.

A: Given,          EF¯ is the perpendicular bisector of CD¯ .

Q: A parallelogram is a rhombus if and only if the diagonals are perpendicular. O True O False

A: Properties of rhombus: A quadrilateral is rhombus iff All four sides are equal. Diagonals bisect…

Q: Prove: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

A: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

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: If ABCD is a rhombus, and mĐ2 = 52°, find mĐ4. %3D A 3 4

A: Given: ABCD is a rhombus and ∠2=52°

Q: Prove that ABCD with vertices 4(-1,3), B(-4,-1), C(1,-1), and D(4,3) is a rhombus assuming it is…

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Q: Given points A(0, 0) and 5(8, 4), show that P(2, 6) is on the perpendicularbisector of AB by using…

A: We have the vertices of the points A and B as Ax1,y1=0,0Bx2,y2=8,4 As we know that mid points of the…

Q: Example Give quadrilateral ABCD with verticesA(4, 7), B(8, 3), C(6,-1), andD(0, 5). Prove: ABCD is a…

A: Given : Quadrilateral ABCD with vertices A(4,7),B(8,3),C(6,-1) and D(0,5). So, Graph is :

Q: Prove that C is on the perpendicular bisector of segment AB.

A: Solution:Given A(-4,-3), B(6,1) and C (5,-11)To Prove: C is perpendicular bisector of ABi.e., to…

Q: Vaughn Pang sketched trapezoid RUIZ on a coordinate plane. RUIZ has vertices located at R(1,4),…

A: Given:In trapezoid RUIZR≡1,4U≡-2,0I≡7,0Z≡3,4To find:Perimeter of RUIZ

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(5, -2,…

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Q: 2. Determine the value of each variable for parallelogram INDY that has diagonals that intersect at…

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Q: Let R be the interior of the parallelogram with vertices (-3, 1), (-1,0), (–1,2), and (1, 1).…

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Q: (c) Consider the parallelepiped with sides: u=(5,-2,1), v=(3, 2, 4), and w=(-6,1,1). V

A: Angle between two vector V and W found using cosine function

Q: The parallelogram (ABCD) has vertices at A(2,-1,4), B(1,0,-1), C(1, 2, 3), and D, then اخترأحد…

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Q: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

A: Given- The diagonals of  a parallelogram are prependicular . To show- That the parallelogram is…

Q: Verify that the points A(0, 3, 2), B(1, 5, 5), C(6, 9, 5), D(5, 7, 2) are the vertices of a…

A: Given points are A(0,3,2), B(1,5,5), C(6,9,5), D(5,7,2).

Q: 6. Prove that quadrilateral LEAP with the vertices L(-3,1), E(2,6), A(9,5) and P(4,0) is a…

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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: Find the coordinates of point P along the directed line segment AB so that the ratio of AP to PB is…

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Q: 1. Rhombus ABCD with vertices A(-3, -2), B(0, 3) C(5, 6), and D(2, 1): (x, y) → (x + 2, y-6) A'L B'…

A: The given coordinates of rhombus is  A-3,-2, B0,3, C5,6, D2,1 The transformation is x,y→x+2,y-6 So…

Q: Is of quadrilateral QRST intersect at P(-3,3). QRST has vertices at Q(4,7) and R(-4,5). What must be…

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Q: Prove that the diagonals of any parallelogram bisect each other. (Hint: Label three of the vertices…

A: Given:- ABCD is a parallelogramTo prove:-AO=CO                 DO=BOProof:-In ∆AOD and ∆COB∡OAD=∡OCB…

Q: Show that the quadrilateral with the given vertices is a trapezoid. Then decide whether it is…

A: Given: The vertices as W1,4, X1,8, Y-3,9, Z-3,3, To show: WXYZ is a trapezoid, To determine: Whether…

Q: ABCD is a rhombus with diagonals that intersect at F. Find the mZADC, if MZABD = 2x + 3 and mZDBC =…

A: It is given that ABCD is a rhombus and m∠ABD=2x+3,m∠DBC=4x-1. Sketch the rhombus as follows:

Q: ABCD is a rhombus with sides AB and BC. If AB : %3D 12x - 2 and BC = 3x + 7. Find CD. CD =

A: In rhombus ABCD, AB = 12x-2 BC = 3x+7 To evaluate : The side length CD

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(7, 2,…

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Q: Quadrilateral RYZP is a RHOMBUS. If RK = 5, RY = 13 and MZYRZ = 67°, find the mZRZP. * R K. z.

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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: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(7, -3,…

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Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(2,…

A: Given points, A(1,1,3) B(2,7,1) C(4,10,-6) D(3,4,-4) Let a,b,c,d, are position vectors of point…

Q: The vertices of quadrilateral PQRS form a square P(0, 0), Q(4, 3), R(7, -1) and S(3, -4). Use…

A: locating the points on the graph we get

Q: Show that the quadrilateral with vertices P(1,2) Q(4,4), R(5,9), and S(2,7) is a parallellogram by…

A: The given vertices of the quadrilateral are: P(1,2) Q(4,4), R(5,9), and S(2,7) Since the diagonal of…