Find the coordinates of the centroid of the triangle with the given vertices F(1, 5), G(−2, 7), and H(−6, 3). Graph the centroid of the triangle

Q: Find the matrix A of the quadratic form associated with the equation. 7x2 + 7y2 + 7z2 + 6xy + 6xz +…

A: We will find corresponding matrix and then its eigen values to determine final equation eliminating…

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: Let g(x) = b,x² + bx + b,x + bg, x E R be a polynomium whose graph intersects the points (-2, 4),…

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Q: Draw a figure that shows the image of the triangle with vertices (0, 0), (1, 0), and (1/2, 1) under…

A: It is given that the vertices of the triangle are 0, 0, 1, 0 and 12, 1. We have to sketch the graph…

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 coordinates of the centroid of APQR with vertices P(-2,5) , Q(4,1) , and R(-2,- 3). The…

A: Explanation of the answer is as follows

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: Use the given transformation to evaluate the integral. (8x + 8y) da, where R is the parallelogram…

A: Given that vertices of parallelogram is −3,9,3,−9,4,−8  and −2,10 And transformation is x=14u+v  and…

Q: F = (-3y, 3x); R is the triangle with vertices (0, 0), (1, 0), and (0, 2).

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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: Use the transformation u = y – 3x, v = y + 6x to evaluate // (2y + 12x) dA on the parallelogram R…

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Q: Use the given transformation to evaluate the integral. (12x + 12y) dA, where R is the parallelogram…

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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: (d) [[x - y dA where R is the triangular region with vertices (3, 10), (3, 0) and (-2, 0).

A: Use double integral

Q: -4 2 -10 -8 -6 -4 -2 2 10 -2 U -4 -8 -10 W 00 6, 6,

A: solution given below..

Q: A. Find an equation of the hyperplane H in R° that passes through P(1; 3; 5; -1,4) and is nomal to…

A: Let's see the concept. Concept:- Equation of hyperplane H in R5 that passes through(p, q, r, s, t)…

Q: (x² +2y) where D is the triangular region with vertices (0, 1), (1,2) and (4,1).

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Q: 7. Find the centroid of a triangle whose vertices are (2, 3), (-4, 6) and (2, -6). В. (0, -1) A. (0,…

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Q: L' M' Which describes how the transformation affects the coordinates of the vertices of trapezoid…

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Q: Use the transformation u = x2 –- y²,v = x² + y² to find ff, xydA where R is the region in the first…

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Q: Calculate , (7xy+ 3e²) dS, where S is the triangle with vertices (0,0, 3), (1,0, 2), and (0, 4, 1).…

A: Given vertices of triangle are 0,0,3 ,1,0,2 ,0,4,1 Let the equation of plane through these points…

Q: In AEFG, L is the centroid. If LJ=9 find EL. H J E K

A: We have given a triangle. In which LJ is the centroid. And we have to find EL

Q: Use the cross product to find an equation for the plane that passes thru the points (1, 2, 3), (4,…

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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: 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: I need help with this questions please. If R is the rectangle with vertices at…

A: F(x,y,z) is a vector field hence,  F = Fxax + Fyay + Fzaz    dr =  dx ax + dy ay + dz az…

Q: 4. Find an equation for the plane in R³ spanned by the points (1,5, 1) and (1, 4, 2).

A: The two vectors are given as v1 = 151v2 = 142 Let xyz∈span{v1 , v2} Then xyz = mv1+nv2= m151+n142=…

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: 21 AATC has vertices at A(-8, -5), T(8, -5), and C(4, 1). Determine the coordinates of the centroid.…

A: The formula to find the coordinates of centroid of a triangle having vertices x1,y1, x2,y2 and x3,y3…

Q: Z is a complex variable, z=x+iy

A: The z is complex variable with z = x + i y , and the given vertices are (0,0),(1,0),(1,1) and (0,1).

Q: Find the matrix A of the quadratic form associated with the equation. 10x2 + 10y? + 10z2 + 10xy +…

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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…

A: Given points are :  P1(1,4) , P2(3,4) , P3(3,6) , P4(1,6). We will first plot those points in a…

Q: Find the vertex of the paraboloid z=x2+4y2−xy+6x−5y+1

A: The paraboloid is of two type, one is elliptic and another is hyperbolic ,  By suitable choice of…

Q: 19. y² dA, D is the triangular region with vertices (0, 1), (1, 2), (4, 1)

A: 19. Given D is the triangular region with vertices (0, 1), (1, 2), (4, 1).We find the given double…

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,&0,6      And centriod G ?      centriod G= x1+x2+x33…

Q: Find // (4x + 5y)dA where R is the R parallelogram with vertices (0,0), (-3,1), (2,4), and (-1,5).…

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Q: Find the matrix A of the quadratic form associated with the equation. 6x² + 6y2 + 6z? + 8xy + 8xz +…

A: Given 6x2+6y2+6z2+8xy+8xz+8yz-1=0

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

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Q: Find the centroid of the triangle formed by joining the points A (3, 2), B (-1, 4), and C (5, -3).…

A: Explained below

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: Give Z(G), the center of G, for G = S3 %3D

A: Definition of Center: Let G be a group. The set of all elements which commute with every other…

Q: AABC is shown below in the coordinats plane with vertices A4, 2), B(4, 6). and C(6, -2). AABC is…

A: We can find the vertices as below

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

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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: 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: 1. F = [2², -x², 0], S the rectangle with vertices (0, 0, 0), (1, 0, 0), (0, 4, 4), (1, 4, 4)

A: As given that,  F→=z2i^-x2j^+0k^ Calculating curl F,…

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…