A quadrilateral has the following vertices given:  P1 (1, 4), P2 (3, 4), P3 (3, 6), P4 (1, 6).  The location of the centroid from the y-axis is equal to

Q: Find the coordinates of the centroid of the triangle with the given vertices. X(1, 4), Y(7, 2), Z(2,…

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Q: Determine the Miller indices of a plane that makes intercepts of (4, 3 and 8) on the coordinate axes…

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Q: Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 3,…

A: Consider the provided question, Let the vertices of the parallelepiped are A, B, C and D.

Q: 3. Rectangle PORS with vertices P(5, 15). Q(15, 15). R(15, 10), and S(5, 10): A- 4/5 4. Rhombus WXYZ…

A: Plot the given points and its scaled version

Q: Rhombus WXYZ with vertices W(1, 5), X(6, 3),Y(1, 1), and Z(-4, 3) in the x-axis W'

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Q: Find a parametrization for the line segment beginning at P,(4, - 7,- 7) and ending at P2(0, - 7,2).

A: The line segment beginning at P1<4, -7, -7> and ending at P2<0, -7, 2>

Q: Find the centroid (ã, §) of the triangle with vertices at (0, 0), (2, 0), and (0, 8). || 18

A: Recall: Centroid of a Triangle with vertices are (x1,y1) , (x2,y2) and (x3,y3) is…

Q: Find the centroid (ĩ, g) of the triangle with vertices at (0, 0), (10, 0), and (0, 9).

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Q: If the circumcentre of a triangle lies at the origin and the centroid is the middle point of the…

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Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: two vertices of the a  triangle ABC are (6,-2) and B(4,3) If the co-ordinates of its centroid be…

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Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,,n2, n2),B(m,,m2,m3),C(r,,r2, 13).

A: Please see the explanation below

Q: Find the points on the cone 2² = x² + y² that are closest to the point (3,-3,0)

A: Cone Equation: z2=x2+y2 Given point: 3,-3,0 To find: the points on the cone nearest to the given…

Q: where P is the parallelogram Spanned by the Vectons 24,13 and <3,3) with tHanformation X=4u+3V and.

A: Given that ∫∫Pe4x-ydxdy where p is the parallelogram spanned by the vectors 4,1 and 3,3 with…

Q: Find the coordinates of the centroid of the triangles whose vertices are: a. (5.7), (1, -3), (-5.1);…

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Q: Prove that the centroid of a parallelogram is the point of intersection of the diagonals of the…

A: The vertices of the parallelogram are (0, 0), (0, a), (b, c), and (b, a + c)

Q: 4. Rhombus WXYZ with vertices W(1, 5), X(6, 3), Y(1, 1), and Z(-4, 3): x-axis

A: Given vertices are: W (1,5)X (6,3)Y (1,1)Z (-4, 3)

Q: Find the point on the sphere  x2+y2+z2=900 that is farthest from the point (−19,−8,11).

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Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: If the coordinates of the mid-points of the sides of a triangle are (1,1) ,(2,-3) and (3,4) .Find…

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Q: Find the volume of the parallelepiped determined by the vertices A(1,1,1), B(4,7,2), C(3,2,1) and…

A: Let the vertex A(1,1,1) be taken as the point from which all measurements are taken. Calculate AB→,…

Q: In space coordinates system, the y-axis consists of all points of the form O (x, 0, 0) O (0, 0, z) O…

A: we know that(x,y,z) is nothing but distace of a point from origin along the x,y,z-axis

Q: Find the centroid of the triangle whose vertices are at points (3,4). (6.-9) and (6,-2). asap pls

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Q: 4) Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0,…

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Q: 2. Find an equation of the sphere that passes through the point (2, 3, –1) and has center (-3, –1, –…

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Q: What are the coordinate planes in three-dimensional space? How are they drawn?

A: The Cartesian coordinate system is used to describe three-dimensional space which consists of an…

Q: Prove that quadrilateral GHIJ with the vertices G(-2,2), H(3,4), 1(8,2), and J(3,0) is a rhombus. YT…

A: solution: the objective is to determine whether the given vertices forms a rhombus

Q: Find the point on the plane 2x + y + 4z = 5 that is closest to the point P(4, 3, 5). (x, y, z) =…

A: We are given a plane 2x + y +4z = 5, and we are asked to find the co-ordinates of the point on the…

Q: Use Green's theorem to calculate where C is the rectangle with vertices (0, 0), (2, 0), (2, 3), (0,…

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Q: If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates…

A: On solving this we will get:-

Q: QuadrilateralPQRShasverticesP(0,2),Q(4,8),R(7,6),andS(3,0). a)ProvePQRSisaparallelogram.…

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Q: 4. Find an equation for the plane in R spanned by the points (1, 5, 1) and (1,4, 2).

A: Given v1 = (1 , 5 , 1)v2 = (1 , 4 , 2) Let xyz be a point in spanv1 , v2 , so there exist m , n…

Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: Find the point on the sphere x²+y2+z²=1225 that is farthest from the point (6,9,24).

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Q: 1. Find the distance from the center of the sphere given by (x-2)² +(y+2)²+(z-1)² = 4 to the point…

A: Given equation of the sphereis x-22+y+22+z-12=4So center of the sphere be 2,-2,1and the given…

Q: Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N(8, 0).

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Q: The center of the sphere whose one of its diameters has end points P;(1,3, –1) and P2(2,-2,1) is |…

A: Given that the endpoints of the diameter of the sphere are P11, 3, -1, P22, -2, 1 To find its…

Q: A cube of cheese from Italy with edge measure of 1 was cut by Mickey using a plane in a manner that…

A: Let us assume the the cordinates OA= OB= OC= 1

Q: Find the centroid of the triangle if the vertices are  (0,0) , (4,0) and (0,6)

A: Given points are         0,0,4,0,&amp;0,6      And centriod G ?      centriod G= x1+x2+x33…

Q: Prove that the centroid of any triangle is located at the pointof intersection of the medians.…

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Q: Find the centroid (, ) of the triangle with vertices at (0, 0), (10, 0), and (0, 2). 19 120 y=

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Q: Use Green's Theorem to evaluate $4x²ydx+2ydy where C is the triangle with vertices (0,0), (1,2), and…

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Q: Use Green's Theorem to evaluate $. xydx + x²y³dy, where C is the triangle with vertices (0,0), (1,0)…

A: Consider the provided question, ∮cxydx+x2y3dy,     where c is the triangle with vertices 0,0, 1,0…

Q: The centroid of a triangle lies at the intersection of the triangle's medians, because it lies…

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Q: calculate Sry³ dA where Ris the vertex of the triangle (0, 2), (1,1) and (3,3 )|

A: The sketch of R is

Q: Find the distance from the point to the plane. (6, 0, —6), т — у %3D 4

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Q: Find the centroid of the triangle whose vertices are  O(0,0) , A(4,0) and B(0,6)

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Q: The distance between the centers of the following two spheres: x2+56x+y2−54y+z2=−1512,…

A: A detailed solution is given below

Q: Find the centroid (ã, g) of the triangle with vertices at (0, 0), (5, 0), and (0, 9). y=

A: In the question it is asked to find centroid of the triangle with coordinates (0,0), (5,0) and…

Q: Find a plane containing the point (3,-7,8) and the tine of intersection of the planes-4z +4y + 4z =…

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