Let the vertices of parallelogram MNPQ be the points M(0,0), N(a,0), P(a+b,c), and Q(b,c). Which equation must hold true if the diagonals of MNPQ are perpendicular?

Q: Consider the shape with vertices (1,3),(4,7),(0,10),(-3,5) translate the rectangle so (1,3) lies on…

A: We need to transform the coordinates.

Q: Let A (-23, 12), B (13,36), and C (23,-1) be vertices of a triangle. Where will the medians of this…

A: Given: vertices of the triangle              A=-23,12 , B=13,36 , C=23,-1To find: to find the co…

Q: The plane through the points (-4,-8,-1), (8,3,5), (7,8,6) has equation Ax + By + Cz= D. If A = - 19…

A: Since plane passes through the given points therefore

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: Calculate the area of the parallelogram with the given vertices: (-1,-2), (2,7), (7,2), (10,11).

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Q: Quadrilateral ABCD has vertices A (1, -1), B (7, 1), C (8, -2) and D (2, -4). Determine whether ABCD…

A: A quadrilateral is a parallelogram if: a) length of opposite sides are equal b) midpoint of…

Q: Suppose a triangle has the following vertices: v1 = (-2, 3, 6) v2 = (4, 5, -1) v3 = (3, 3, 0)…

A: Consider a triangle T defined by its three vertices r1, r2, and r3. Each point r located inside this…

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: In a rectangular grid with corner points (0, 0), (0, m), (n, m) and n, 0), determine the number of…

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Q: Verify that the points are the vertices of a parallelogram, and find its area A( 1, 1, 3), B(-5, 7,…

A: let the points be A1,1,3 , B-5,7,1 , C-3,10,-6 , D3,4,-4 verify that the points are the vertices of…

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…