For the parallelogram ABCD with vertices A(0, 0), B(a,0), C(a+b, c), and D(b,c) to be a rhombus, it is necessary that a = √b²+c². Select one: True False

Q: Three vertices of parallelogram ABCD are A(-5;0), B(0;1) and D(-1;3). Evaluate the length of…

A: Given 3 vertices of the parallelogram are  A-5,0 ; B0,1 and D-1,3  Let the fourth vertex be Cx,y…

Q: the line a1x+b1y+c1=0 and a2x+b2y+c2=0 cut the coordinate axes at concyclic points,then prove that…

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Q: Find the perimeter of the polygon with the vertices Q(−3, 2), R(1, 2),  S(1,−2),Q(−3, 2), R(1, 2),…

A: Perimeter of polygon = Sum of length of all sidesLet A(x1, y1) and B(x2, y2) . Then,   Length of…

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: Use slopes to show that the quadrilateral with vertices at (1, 3), (-5/2, 2), (-7/2, 4), and (2, 1)…

A: Given that Vertices of quadrilateral are A1, 3, B-72, 4, C-52, 2 and D2, 1   It is known that the…

Q: Determine the line of intersection between the following planes 12. 5x+2y-7= 9 and -2x+8y +9= = 3.

A: Given: The planes are 5x+2y-7z=9 and -2x+8y+9z=3 To find the line of intersection of the given…

Q: order for the parallelogram to be a rhombus x= 3x+11 x+23

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Q: If AB=3x+1, DC = 2x+7, AD = 2x-1, BC = x+5 and x = 6, prove that ABCD is a parallelogram

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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: Graph the points A(-5, 0), 5(3, 2), C(5, 6), and D(-3, 4). Then showthat ABCD is a parallelogram by…

A: Given  The points A(-5, 0), 5(3, 2), C(5, 6), and D(-3, 4) , and  ABCD is a quadrilateral .

Q: 10. Paralleogram ABCD has vertices A(-1,4), B(3,2), c(3,-4), and D(-1,-2). y A(-1, 4) B(3, 2) 4-2 2…

A: Given, Parallelogram ABCD with vertices  A-1, 4B3, 2C3, -4D-1, -2  We have to find the equation…

Q: The point (4,3) is. the point of the intersection of the diagonals of parallelogram and two of whose…

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Q: Evaluate fS, 6x² – 40y dA, where D is the triangle with vertices (1,1), (5,0) and (5,3).

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Q: Use an algebraic proof to show that the points A(-3, 1), B(0, 4), C(0, 2), and D(-3, -1) form a…

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Q: Let A (1, 2, -1), B (3, -1,4) and C (2,6,2) be three vertices of parallelogram ABCD a-Find the…

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Q: 13. Prove that the three points (-3, 2, 4), (6, 1, 2), and (-12, 3, 6) are collinear by using the…

A: To solve the following problem

Q: If the lines a₁x + b₁y+C₁ = 0 and a₂x + b₂y + C₂ = 0 cut the coordinate axes at concyclic points,…

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Q: :Prove that (4,-1).(6,0).(7,2)and (5,1) are the vertices of a rhombus.Is it a square?

A: In a square the sides are perpendicular but in a rhombus they need not be. All sides are of equal…

Q: Determine whether the four vertices form a parallelogram: P(1, - 4), Q(3, 11) , R(6, 11), S(4, - 4)…

A: Diagonals of parallelogram bisect each other.So we will find  mid points of each diagonal and see if…

Q: Two birds sit at the top of two different trees. The distance between the first bird and a…

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Q: 8) Determine whether the given vertices represent a parallelogram, rectangle, or rhombus. ВС-1,-1),…

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Q: (1) 100 (20)

A: True or false: The fourth vertex of the parallelogram shown is (a+c, d)

Q: Consider the points A (-2, 2, −3), B (-4, -2, -3), and C (0, 4, 3). Find all the points D so that…

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