The corners of a quadrilateral are (4, 0), (12, 4), (10, 8), and (4, 4). How far is its centroid from the y-axis? O 5.67 O 6.67 O 7.67 O 8.67

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2,1,0) Q(2, 3, 2)…

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Q: Use the new command from Example 3 above to find the volume of the parallelepiped formed by vectors…

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Q: In AABC, X is the centroid. If CW = 15 , find XW. %3D

A: Given,           In △ABC, X is the centroid and CW¯=15

Q: Use drawings as needed to answer the given question

A: (a) In Euclidean geometry, if two or more than two points lie on a line close to or far from each…

Q: Let T be the tetrahedron with vertices (2, 0, 0), (0, 3, 0), (0, 0, 5) and the origin. Write (a, y,…

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Q: Find the volume of the parallelepiped whose adjacent axes PQ, PR and PS where P (1,-2, 2), Q (1, -1,…

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Q: B) Find the volume of the parallelepiped (box) determined by u, v, and w while: u = 10i + 20j + 50k,…

A: I am going to solve the given problem by using some simple geometry to get the required result.

Q: Find the centroid of the given region. y = 2-x? y = x A (3/22,45/61) В) (5,15) c) (5/14,38/35)…

A: Centroid is x¯,y¯ , where, x¯ = 1A∫ab xfx-gx dx  and y¯ = 1A∫ab 12 fx2-gx2 dxand A = ∫ab f(x)-g(x)…

Q: Find the surface area of the tetrahedron bounded by the coordinate planes and the plane 8x + 12y +…

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Q: A quadrilateral has the following vertices given: P1(1,4),P2(3,4),P3(3,6),P4(1,6).the coordinates…

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Q: Find the centroid (x, y) of the triangle with vertices at (0, 0), (10, 0), and (0, 2). 18 15 X=

A: Consider a triangle with vertices at (0,0),(10,0) and (0,2)

Q: The volume of the pyramid formed in the first octant by the plane 6x + 10y + 5z-30 = 0 is: О 45 О зо…

A: We can solve as follows

Q: Find the centroid of the shape with endpoints (0,0),(0,4),(-2,4).(-2,6),(2,6),(2,3),(4,3) and (4,0)…

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Q: Every triangle has a balancing point, called the centroid. O True O False

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Q: Z is the centroid of AUVW. What is UY if UZ = 8? O A. 4 о с. 6

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Q: In the triangle below, O is the centroid. Find the length of median XP. 3x 2x-7 Y XP

A: Given, OP = 2x - 7 OX = 3x  So, According to the figure XP = OX + OP      = 3x + 2x - 7       = 5x -…

Q: Find the volumes of the regions. The wedge cut from the cylinder x2 + y2 = 1 by the planes z = -y…

A: Given Data The equation of a cylinder is x2+y2=1. z=-yz=0   Determine the interval of x and y,…

Q: Use a scalar triple product to find the volume of the parallelepiped that has u, v, and w as…

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Q: Find the volumes of the regions

A: The Volume of  the wedge, where D is the solid and R is the region, is calculated as,…

Q: A power cable is to be fitted under a road and can be represented on 3D Cartesian axes as below with…

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Q: Sections ABCD is a quadrilateral having the given coordinates A(2, 3), B(8, 9), C(11, 3), and D(11,…

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Q: Find the point lying on the intersection of the plane x + y +z = 0 and the sphere x2 + y2 + z? = 25…

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Q: Find the volume of the parallelepiped (box) determined by u, v, and w. u V i+ 3j 4i - j+4k 2i + 4k

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Q: Evaluate (y + Vx) dA, where R is the triangular region with vertices (0, 0), (1,0), and (0, 1). R

A: The solution starts from step 2. The information presented below will be helpful to understand the…

Q: Find the area of the surface. The part of the cylinder y2 + z2 = 9that lies above the rectangle…

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Q: 12 Which equetilon describes a crcle with center (4, -7) and radius 97 A (x+4) +(y-7) -81 b. (x-4)+y…

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Q: Z • W Y. T. U. 10. What is the intersection of the two planes? 11. Are points T, Z, U, and W…

A: To answer the given questions using the given figure.

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2, 1, 0) Q(2, 3,…

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Q: dA where R is the quadrilateral with the 5: Evaluate RI+y vertices (1,0), (4,0), (0,1), (0,4) using…

A: The solution are next step

Q: In triangleRST, the medians are RM, SN, and TP. If RM = 9, SN = 12, and TP = 16, find the distance…

A: median of the triangle

Q: B) Find the volume of the parallelepiped (box) determined by u, v, and w while: u = 10i + 20j + 50k,…

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Q: Draw an image of quadrilateral ABCD on the coordinate plane reflected over the y-axis

A: when Quralatral reflected over y-axis then y coordinate does not change only x coordinate change

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

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Q: Which is the equation of a sphere with a center at (1,0,-2) with a volume of 36(pi)(u^3)? a.…

A: We first defined the equation of sphere and centre,volume . Using this formula we have equation (a)…

Q: Try to visualize the set of all points (x, y, z)in a coordinate space that are twice as far from the…

A: a) Suppose the distance between two points  A(x, y, z)  and the origin   Plug into the distance…

Q: Find the volume of the box (parallelepiped) that is determined by u = i + 2j - k, v = -2i + 3k, and…

A: Solution:-  The given vector is  u→=i+2j-kv→=-2i+0j+3kw→=0i+7j-4k

Q: find the centroids of the triangleswhose vertices appear . Assume a, b > 0. (0, 0), (1, 0), (0,…

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Q: What are the coordinates of the center of dilation for the dilation shown? The center of dilation is…

A: It is given that Two triangles are given under a dilation. Quadrilateral D’E’F’G’ is the image of…

Q: Let T be the tetrahedron with vertices (3, 0, 0), (0, 2,0), (0, 0, 5) and the origin. Writel II|…

A: Follow the steps to find the upper limit of x and z to solve the problem.

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2,1,0) Q(2,3, 2)…

A:

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2, 1, 0) 2(2, 3,…

A: Follow next step

Q: Let T be the tetrahedron with vertices (5, 0, 0), (0, 2, 0), (0, 0, 5) and the origin. Write II|…

A: Given T is a tetrahedron with vertices (5,0,0) , (0,2,0), (0,0,5) and  (0,0,0)…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2, 1,0) Q(2, 3, 2)…

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Q: Change from rectangular to spherical cooordinates (√3, 1, 2√3)

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Q: Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians,…

A: We can find the centroid as below using the required formula.

Q: Consider AB in the coordinate plane below. 10 7 5 4 3. 2 A B 6 7 89 10 10-9 -8 -7 -6 -5 -4 -3 -2 -1…

A: i am going to solve the given problem by using some simple geometry to get the required result.

Q: In the triangle below, O is the centroid. Find the length of median XP. 3x 2x-7 XP

A: Given, Where, O is the centroid. XO=3xOP=2x-7

Q: Find the centroid (, j) of the triangle with vertices at (0, 0), (8, 0), and (0, 9). x=

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Q: find the centroids of the triangleswhose vertices appear . Assume a, b > 0. (0, 0), (a, 0), (0,…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.