Quadrilateral JOSH has points J(2,8) O (5,10) S( 4,4) H ( 7,6): (x,y) -- (x +2, y- 5)ldentify the Coordinates of the image J'

Q: Find the distance between the point (0,0,0) and the plane 2x – y + 2z = 4

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Q: Find distance from point (-6, 3, 5) to the plane – 2y – 4z = 8| -

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Q: 2. The plane containing the point (-8, 3, 7) and parallel to the plane given by 4x+8y-2z=45.

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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: Where does the line through (1,0, 1) and (4,– 2,2) intersect the plane x+y+z = 6?

A: It can be assumed that the vector for the coordinate 1,0,1 is 1,0,1 and the vector for the…

Q: Determine the location of a point (x, y, z) that satisfies the condition  ∣y∣ ≤ 3

A: If ∣y∣ ≤ 3 the point lies with in 3 units from xz plane on left side if y < 3 , or within 3 units…

Q: Q1: Find the parametric rquations of the line that passes through the point P(4,2,-3) and Q(-3,2,2).…

A: Here we have to find the parametric equation of the line that passes through the point P(4,2,-3) and…

Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, - 1, 2) is parallel | to the line x=…

A: Given that points are (2,1,-1), (0,-2,0) and (1,-1,2) The parametric equation is,…

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 distance between point (-1,1,3) and the plane 5x-5y+3z=25

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Q: 5. Find the exact value of distance from the point (1, -3, -1) to the plane 2x-y+3z = -5

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Q: Calculate the distance between the points L= (-9, 8) and J=(-1, 1) in the coordinate plane. %3D Give…

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Q: Find the shortest distance from the point (1, 5, -5) to the plane 2x + 9y - 3z = 6, using two…

A: Given point is 1,5,-5 and plane is 2x+9y-3z=6

Q: Find the point on the plane x−3 y+3 z =−8 that is closest to the point (−2,−2,0) .

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Q: 12) The distance from the point S(-10, –4, –6) to the plane -9x + 2y + 6z = 4

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Q: 7. Find the distance between the point (- 3, 2, 1) and the plane with equation x - 2y + 3z = 5

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Q: Where does the line through (1,0,1) and (4,-2,2) intersect the plane x+y+z=6?

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Q: The distance between the point ( 9,8,3) and the plane x + y – 2z = 5 is .... %3D

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Q: The plane containing the point (0,7,-2) and parallel to the plane -x + 8y + 6z = Ax+By+Cz = D. 4 has…

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Q: The plane through the points (2, 1, –1), (0, –2, 0), and (1, – 1, 2) is parallel to the line x=1-t,…

A: Equation of plane passing through x1, y1, x2, y2, x3, y3 is given by,…

Q: Which graph shows the intersection curve, in the first octant, between a cylinder of equation: (x −…

A: In this question, we need to find the curve which describes the intersection of the surfaces.…

Q: Calculate the shortest distance between the point P = (3, 2, 2) and the plane 5x+y-2z = 3. (Do not…

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Q: Find a parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it using…

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Q: Find the point P nearest to Q = (−1, 3, −1) on the planex − 4z = 2

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Q: Find the distance from the point to the plane (2,-3,4) , x+2 y - 2 z = 13

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Q: 1. y = x², x = 0 , x = 2, y = 0, about the x – axis - 2. V9 - y?, у %3 1, у %3 3, а %3D 0, about the…

A: Use formula to calculate volume

Q: Determine the location of a point (x, y, z) that satisfies the condition z = −5

A: The condition is z = −5

Q: -axis. 5. Evaluate dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2, 0, 0),…

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Q: find distance between plane(6x_2y_z+4=0)and point (3,2,1) P 3:08

A: Given,           The plane is 6x-2y-x+4=0 and the point is 3,2,1.

Q: Find the distance from the point (2,-3,5) to the plane passes through the points (1,0,-3), (3,4,-6)…

A: (b) Given point P2,−3,5 and a plane passes through the points 1,0,−3, 3,4,−6 We have to find the…

Q: Q1/: Find the distance between plane (6x - 2y - z +4 = 0) and point (3, 2, 1). (6 marks)

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Q: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…

A: Given x=-2, y=4+2t, z=-3+tfor finding intersection with xy-plane , set z-coordinate…

Q: Find a parametrization for the line perpendicular to (4,-1,1), parallel to the plane 4x+y-8z=1, and…

A: The parallel line through the point has the vector equation L = < 1,0,5 > + t < a, b, c…

Q: The line through the point (1, 0, 6) and perpendicular to the plane a + 3y + z = 5

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Q: 4) Find the distance from the point (1, 2, – 1) to the plane 2x+y- 2z = 1.

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Q: 5. What are the coordinates of the centroid of triangle FGH: F(6,-1), G(12,4), H(15,-2)?

A: follow next step

Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: Find the intersection of the two planes with equations 3(x – 1) + 2y + (z + 1) = 0 and (x – 1) + 8y…

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Q: Determine the location of a point (x, y, z) that satisfies the condition xyz > 0

A: In four of the eight octants xyz>0 1) x>0, y<0, z<0 (2) x<0, y>0, z<0 (3)…

Q: Determine the distance between the point (-1, 2, 1) and the plane 2x +14y -5z = 7.

A: The distance between a point (x1, y1, z1) and a plane Ax+By+Cz=D is given by…

Q: 12. Find the distance between the point (3,-2,7) and the plane 4x – 6 y + z = 5.

A: The equation of plane is 4x-6y+z=5 and the given point is 3,-2,7. The distance between the point and…

Q: 2. Obtain an equation for a plane a that includes straight line(2--5) and 1: point(-2,1,1)

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Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, -1, 2) is parallel to the line x 1-t,…

A: equation of plane for non collinear points , x-x1y-y1z-z1x2-x1y2-y1z2-z1x3-x1y3-y1z3-z1 we will use…

Q: Q = (-1,3,–1) on the plane Find the point P nearest to x – 4z = 2

A: Given, Q=(-1,3,-1) x-4z=2 (equation of plane) x-4z-2=0

Q: Determine the distance between the point (-1, 2, 1) and the plane 2x +14y -5z = 7

A: We know that the distance between a point (x1, y1, z1) and a plane Ax+By+Cz = D is…

Q: BThe distance from the point (-1, -2, 3) to the plane 2z = - 4x + 5 is [b] (input exact value in…

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Q: Find a plane through the point Po(2, 1, -1) and perpendicular to the line of intersection of the…

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Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y -z = -2?

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Q: 5. Find the distance from the point (4, -3, 6) to the plane *-2y+z=1

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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.