Find the equation of the perpendicular bisector of side of the triangle having vertices A (-1,-3),B(5,-3) and C(5,5) and prove that they all meet at a point.

Q: Find b and c so that y = - 8x + bx + c has vertex (0, – 1). %3D %3D c =

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Q: Of all the points on the graph of z = 10 - x^2 - y^2 that lie above the plane x + 2y + 3z = 0, what…

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Q: Find the point on the sphere x²+y2+z2=2304 that is farthest from the point (1,-18,-27).

A: d  = x-12+y+182+z+272d2 = x-12+y+182+z+272fx, y, z = x-12+y+182+z+272subject to the constraintgx,…

Q: If two vertices of an equilateral triangle are at (0, 0) and (2a, 0), what point is the third…

A: The given diagram is, Since, ∆ABC is equilateral triangle. AB=BC=AC. ⇒AB2=BC2=AC2 Suppose point A…

Q: On the line of intersection of the planes y+2z=12 and x+y=6, find the point (a,b,c) that is closest…

A: Given planes, y+2z=12andx+y=6 Consider the point of intersection be x,y,z.

Q: |Find the coordinates of the intersection of the diagonals of paralle with vertices P(2,5), R(3,3),…

A: Follow the procedure given below.

Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

A: Given points are , (-4,9) , (-2,6), (3,-6)Let P =(-4,9)Q = 9-2,6)R = (3,-6)Hence peremeter = Length…

Q: Show that the points A(2, -1), B(1, 3), and C(-3, 2) are verticesof a square, and find the fourth…

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Q: Show that (km) is the number of paths in a square grid from (0,0) to the point (m,n) on the diagonal…

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Q: Find b and c so that y = – 5z² + bz + c has vertex (9, 1). c =

A: The given equation y=-5x2+bx+c has a vertex at (9, 1). The given equation is an equation of a…

Q: Find the value of x in the rhombus. (3x - sx)° (4x - 24).

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Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

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Q: Find the value of x in the rhombus. (3x²-6x) (4x² -27) ° X=

A: According to properties of rhombus, The diagonal bisect the angle. Opposite angles are equal.

Q: Show that the points A(3,-2,4)B(1,1,1,) and C(-1,4,-2) are collinear

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Q: Find the coordinates of the intersection of the diagonals or Parallelogram PRYZ with given vertices.…

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Q: Find the point on the sphere x2+y2+z²=900 that is farthest from the point (14,-5,-1).

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Find an equation for the plane through P0(-3, 0, 7) perpendicular to n = 5i + 2j - k.

A: given that the plane passes through (-3,0,7) perpendicular to n=5i+2j-k. we need to find the…

Q: ) Find the equation of line of intersection of the following planes 3x – 4y + 4z – 29 = 0 , 6x – 8y…

A: Explanation of the solution is given below...

Q: Prove that the point 2a +b-c, 5a -b+ 2c and 8a – 3b+5c are collinear.

A: Given, 3 vectors or points, A(2,1,-1) B(5,-1,2) C(8,-3,5)

Q: 1. Find the equation of the perpendicular bisector through: (2,-5) and (3,1)

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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: Find the areas of the parallelograms whose vertices are A(1, 0), B(0, 1), C(-1, 0), D(0,-1)

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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: Verify that parallelogram ABCD with vertices A(-5, – 1), B(-9, 6), C(-1, 5), and D(3, – 2) is a…

A: We can verify this as below using the diagonals.

Q: Find the shortest distance between the point A(2, 5, –7) and the plane 3x – 5y + 6z = 9.

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

Q: 10. Quadrilateral ABCD with vertices A(-4, -1) B(0, -2), C(-1, -6), and (-6, -3) in the y-axis. A'(…

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Q: :Prove that (4,-1).(6,0).(7,2)and (5,1) are the vertices of a rhombus.Is it a square?

A: In a square the sides are perpendicular but in a rhombus they need not be. All sides are of equal…

Q: Let the vertices of parallelogram MNPQ be the points M(0,0), N(a,0), P(a+b,c), and Q(b,c). Which…

A: Consider a parallelogram MNPQ with vertices  M(0,0), N(a,0), P(a+b,c), and Q(b,c)

Q: Find the equation of the plane through the point P = (3, 2, 5) and parallel to the plane a + 3y+ 3z…

A: Given: Line is parallel to x+3y+3z = 5 Equation of the plane parallel to the plane x+3y+3z = 5 is…

Q: Which of the points A(-4,0,–1), B(3,1,–5), and C(2,4, 6) is closest to the yz-plan Which point lies…

A: Given: A(-4,0,-1)  B(3,1,-5)  and C(2,4,6) To find: Which is closet to the yz plane Which is lies on…

Q: If this trapezoid is moved through the translation (x+3, y-2), what will the coordinates of B' be?

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Q: Find an equation of the plane each of whose points is equidistant to the point H(4, 2, 5) and to the…

A: Basic 3D Geometry problem

Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

A: We know that,The peimeter is equal to the sum of thelengths of the sides, which can becalculated by…

Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

A: We know that,The perimeten is equal to the sum of thelenathe of the sides , which can becalculated…

Q: If two planes intersect, is it guaranteed that the method of setting one of the variables equal to…

A: Let say one the intersecting two planes is Ax + By + Cz =D When we put z = 0 the Plane reduces to…

Q: How can we recognize if the two planes were parallel or not

A: Consider the vector equation of the two given planes as, r→·n1→=d1r→·n2→=d2 Here, n1→ and n2→ are…

Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x-2ky + 5z = 0…

A: Two planes are perpendicular iff their normal vectors are orthogonal

Q: The plane containing the point (-4,1,3) and parallel to the plane 4x + 7y – 3z = 2 has equation Ar +…

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Q: B. If the two planes ax-4y - 9z = 4 and perpendicular. Find the value of a. x-2xy + 3z = 1 are

A: Topic = Geometry

Q: Determine whether the planes are parallel, perpendicular, or neither. 7x + 7y + 7z = 1, 7x – 7y + 7z…

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Q: Fix one vertex at (0,a) in the (x,y)-plane and move another vertex along the x-axis. Show that the…

A: Given: A fixed vertex 0,a A second vertex moving along the x-axis. To show: The locus of the third…

Q: Find b and c so that y 1x? + bx + c has vertex - (– 2, 0). С —

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Q: Square QRST has two vertices at Q(-9, 5) and R(-7, 7). Which could be the coordinate of the vertex…

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Q: Graph the first-octant portion of each plane. 4x + 2y + 3z = 24

A: We have to find the graph the first-octant of the plane. To find x- intercept of the plane put y=0…

Q: 9. Square ABCD with vertices A(-7, 5). B(-4, 7), C(-2, 4). and D(-5, 2): 90° counterclockwise

A: To graph the square with given points A,B,C,D.

Q: Which of the following are symmetric equations for the line of intersection of the planes 2x+y+−6z=2…

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Q: A rectangle has a vertex at J(2, 2), H(4, −2), and G(−2, −5). What are the coordinates of the fourth…

A: You know that the diagonals of a rectangle bisect each other.