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

Q: -3- Identify ALL the new coordinates of polygon ABCD after a translation of 2 units up and 4 units…

A: I'm providing hand written solution for better understanding. It's translation of coordinate…

Q: Two cars are traveling on two different roads that are perpendicular to each other. On a coordinate…

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Q: Find the coordinates of a rectangle with corner points at A: (2,4), B:(2,8), C: (5,8), and D: (5,4),…

A: We have to find co-ordinate after translating 6 units up and 2 units left

Q: how that the point (1,0,-1) is the centre of the sphere passing through…

A: Let O=(1,0,-1), A=(1,8,-8) B=(-9,0,5) C=(7,-8,-1) D=(-7,0,7) It is enough to show that…

Q: The area of the triangle with vertices V141 P (1, 5, 2), Q (0, 0, 0), R (3, 5, 1) is

A: Here, PQ = <-1, -5, -2> and QR = <3, 5, 1>. Now,         -1-5-2×351=-5· 1--2· 5-2· 3--1·…

Q: Square ABCD with vertices A(-4,3), B(-2,3), C(-2,1), and D(-4,1) using a scale factor of k = 3 and…

A: Let T denote the scaling by factor 3 centered at (-7,5). Now the coordinates of an arbitrary vector…

Q: Given: J= L M L is the midpoint of KN Prove: K Statements Reasons 1) J LM 1) Given 2) L is the mp of…

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Q: write the quation of the perpendicular bisector that gose through the lie segment with end points of…

A: The perpendicular bisects will be passing through the midpoints of the given points A(4,-1) and…

Q: If (a,B.y) is a point at which the surface x2+y2-z²-2x+12=0 has a horizontal tangent plane, then y|…

A: As per guidelines, we will solve first question only. Let α,β,γ be the point on the surface…

Q: A triangle has vertices at A (1, 6), B (-4,1), and C (0, -2). What are the coordinates of each…

A: Given: Vertices of triangle are: A = ( 1 , 6 ) B = ( -4 , 1 ) C = ( 0 , -2 ) To find: Co-ordinates…

Q: 5 Find the distance between the points (3,-2) and (6,4) a) V85 units 9.219 go to station 7 b) v79…

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Q: Sketch the second order spline that fits the end points PO (0,0), P2(9,4) and tangents intersection…

A: Here we need to sketch the second order spline that fits the end points P0 0,0, P2 9,4 and tangents…

Q: What is the distance between the origin and the point (4, 3, 3)

A: To find the distance between the origin and the point (4, 3, 3)

Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

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Q: *Challenge: For a given triangle, if the centroid is at (-2,5) and the orthocenter is at (-8,13),…

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Q: Find all values of x so that the triangle with vertices A-(4, 4, x), B-(7, 6, 0), and C=(5, 5, 2)…

A: Here we have to find values of x for which area of triangle is 1.

Q: What is the distance from the point (1,9,3) to the xz-plane?

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Q: Find the area of a parallelogram in 3-space when the adjacent sides are A` =2i`+4j`-3k` and B`=…

A: area of a parallelogram in 3-space when the adjacent sides are A` =2i`+4j`-3k` and B`= i`-2k`