The triangle P(1, -4), U(5, 0) and N(2, 1) is reflected over the y-axis. What are the coordinates of the new points? P' [Choose ] N' [Choose] U' [Choose ]

Q: An ant is walking on the xy-plane is such a way that its distance to the point (2, 4) is always the…

A: Solution: Let the point P(x,y) is the position of Ant and given that the distance from P(x,y) to…

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

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Q: 2)Passes point (1,3,7) and orthogonal to xy- plane.

A: The line which is orthogonal to x-y plane is lies on z-axis. Therefore the direction ratio's of the…

Q: find a parametrization of the curve. The line passing through (1, 0, 4) and (4, 1, 2)

A: Given: A line is passing through the points 1, 0, 4 and 4, 1, 2.

Q: Find a parameterization for the line segment joining points (0,3​) and ​(6​,0) using the angle θ in…

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Q: (-6, 4) and (2, 9) %3D AX : %3D Ay Slope = %3D AX

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

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Q: What is the image of the point (2,-3) after the transformationr y-axis 1) (2,3) 2) (-2,-3) 3) (-2,3)…

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Q: 6. Determine the distance from the point (2, -1, 5) to the plane 3x - 3y + 5z = 8.

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Q: 9. Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

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Q: What are the new coordinates of the point (11, 22) under the dilation (x, y) → (2x, 2y)?

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Q: 11) Find the distance between point A(-3, 1,1) and the line of symmetric equations x = -y = -z.

A: This question is related to coordinate geometry, We will solve it using given information.

Q: A robot begins moving on a linear path at (2, 1). When it reaches (5, 2) , the robot turns 90°…

A: The robot begins moving at (2,1) and reaches at (5, 2) taking a linear path. So, the equation of a…

Q: 1 What is the image of the point (-4,-2) after the reflection over the line y = - -X- 1?

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Q: Find the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10.

A: Given,           The distance between the point 2,-4,3 and the plane 5x-2y+z=10.We know that,…

Q: 4 Find a parametrization for the line segment with endpoints (-1,3) and (3,-2).

A: 4) To find the parametric equation of line segment with endpoints (-1,3) & (3,-2)

Q: Find the orthogonal trajectories of the family of circles with center at the point (0, 1) and radius…

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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: Find the shortest distance from the point P(2,-1, 1) to the plane with =quation x - y + 2z = –1 and…

A: Shortest point of the given plane and point P.  Distance from the point P and Q

Q: Compute x²z ds where Cis the line segment from (0,6,–1) to (4,1,5).

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Q: A robot begins moving on a linear path at (2,1). When it reaches (5,2), the robot turns 90°…

A: Linear equation

Q: y -6- 4- 3- 2- 1- -3 2 -1 0 12 3 4 5 6 -1- -2- R -3- your work on question 10, classify this…

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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: Find the number of points in the xy-plane with integer coordinates located at a distance 5 from the…

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Q: A robot begins moving on a linear path at (2, 1). When it reaches (5, 2), the robot turns 90°…

A: We have to find the y-coordinate.

Q: A robot begins moving on a linear path at (2,1). When it reaches (5,2), the robot turns 90°…

A: This is a problem related to linear coordinates. based on the diagram shown in solution we will…

Q: ry = 10, z = 8, x = 9, y = 0, (i) about the z- and about the y-axis;

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Q: Compute the original coordinates with respect to x and y axes if the translated coordinates of this…

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Q: Obtain the dirfferential equation of the family of curves:  1. All circles passing through the…

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Q: What are the new coordinates of the point (6, 15) under the dilation (x,y) → (3-3)?

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Q: A line, passing through point (6, 3, 2) and is perpendicular to the xy-plane. Find a point on this…

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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 the minimum distance from the cone z = 2x2 + y2 to the point (-6, 4, 0).

A: To find the minimum distance first write distance function. Which is the square distance from  .

Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: What is the distance between the point (4,-&, 1) and the plane 5x-z= 2y+5?

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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: 5. Parallelogram RSTU with vertices R(-2, 3), S(2, 4), T(2,-3), U(-2,-4) over the line y = x ty 6.…

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

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Q: What are the projections of the point (6, –3, 5) on the coordinate planes? On the xy-plane: ( On the…

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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: Calculate the distance between the points M=(-9,8) and L=(-1, 1) in the coordinate plane. Give an…

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Q: 3. Find how many roots the equation 2z4 – 323 + 3z² – z + 1 = 0 - - has in the right half-plane Rez…

A: Given: 2z4-3z3+3z2-z+1=0

Q: Which of the following is the equation with center (-9, 8) Major axis = 10? %3D 20 and minor axis…

A: To find the equation of the vertical ellipse with center (-9,8) . Major axis = 20 and minor axis =…

Q: Write the equation of the plane passing through point (3, 8, 3) that is parallel to the xz-plane.. X…

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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: Show that the locus of the point whose distance from Y-axis is thrice it's distance from (1,2,-1) is…

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Q: ) Find an equation of the tangent plane to the paraboloid defined by -- 4x² + 5y² at the point (,-2,…

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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.