A point moves so that sum of the squares of its distances from the vertices of a triangle is always constant. Prove that the locus of the moving point is a circle whose centre is the centroid of the given triangle.

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: 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: Find a parametrization of the line through P = (4, 9, 8) perpendicular to the yz-plane.

A: Equation of Linethe Line through P =(x0,y0,z0) in the diresction of vector v→=(a,b,c)is defined…

Q: Find the least squares approximating parabola for the given points. (-2, 0), (–1, –11), (0, –10),…

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Q: Determine the set of points satisfying the condition described by Iz – 2i| + |z + 4i| express in the…

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Q: The set of all points in a plane the sum of whose distances from two fixed points is constant is…

A: We have to fill the blanks The set of all points in a plane the sum of whose distances from two…

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

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Q: Find the orthogonal trajectories of the family of ellipses with centers at (0, 0) and two vertices…

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Q: 4 and the plane Find the point on the curve of intersection of the paraboloid x- + y- x - y + 2z = 0…

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Q: Defined byT (x, y, z) = (y+2z, –2x+y+2z, –3x– y+52), is diagonalizable.

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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: prove Theorem 4P.1 Theorem 4P.1 There are exactly six lines in the four-point geometry.

A: The known fact is that in four point geometry, any two distinct points have exactly one line on both…

Q: Find all the planes parallel to the plane passing through the points(1, 2, 3), (1, 2, 7), and (1, 1,…

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Q: The point (-2,0,8) is. A. In die xy-vlak O In the xy-plane B. In die yz-vlak O In the yz-plane C. In…

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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: Suppose a plane containts the point P = (1, 2, 3) and vectors å = (4, 1, 0) and b = (6, 0, 1). Use…

A: Solution

Q: Find 3 non-collinear points in the plane ax+by+cz+d=0. (Hint: Set two variables to zero for each…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Line AB 100 mm long is 30 degree and 45degree inclined to HP & VP respectively. End A is 10 mm above…

A: Steps to find HT: Draw xy, one projector and locate VT on it. Draw locus of a110 mm above xy. Take…

Q: Find a parametrization for the line SEGMENT between (- 5, 7, 6) and (2, – 6, – 9). |

A: Parameterizing a line segment, which joins the points (x1,y1,z1) and (x2,y2,z2), helps in obtaining…

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: Use the Lagrange multiplier method to find the point of the plane 4x-5y+3z=1 with less distance to…

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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: Use Lagrange Multiplier to find the Point P (x,y,z) closest to the origin on the plane containing…

A: The equation of the plane passing through the three points can be obtained using the matrices. The…

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

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Q: Find the particular number of orthogonal transectories of x2+cy2=1 passing through the point (2,1)

A: Given equation is x2+cy2=1........1. We have to find the particular number of orthogonal…

Q: Compute the intersections of the curve xy = 1 and the lines x +y = 5/2, x+y = 2, x+y = 0, x=0 , x=1…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Sketch the following Cartesian products on an x, y-plane. (2) {2, 4, 6} × {0, 1, 2} (b) [0, 2) x {1,…

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Q: Discuss the hyperbolic geometry of spacetime in comparison to circular geometry of 3- vector space.

A: Query- Discuss the hyperbolic geometry of spacetime in comparison to circular geometry of 3- D…

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: Determine the set of points satisfying the condition described by |z – 3| + |z + 3| = 10 Then…

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Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: Given: The maps [0, 1] x [0, 1] to the parallelogram in the XY-plane spanned by the vectors (2, 3)…

Q: Which of the following point is the projection of the point (0, 4, 2) on the yz-plane?

A: In this question we have to find the projection of the point on the yz-plane.

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

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Q: Suppose there is a collection of three or more two- dimensional vectors. Provide an argument…

A: Collection of two dimensional vectors mean those vector having i and j components.

Q: If a point moves on a plane is such a way that the sum of its distances from two fixed points on the…

A: Let, x,y be a point on the locus.p,q and r,s be two points.distance between x,y and p,q…

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: Show that the two planer diagram represent the homeomorphic surfaces

A: Given:-                 Show that the two planer diagram represent the homeomorphic surfaces

Q: The equation of a surface, with respect to an orthonormal coordinate system for three-dimensional…

A: Every surface equation with respect to an orthonormal coordinate system is written in a matrix form…