In the coordinate plane, right triangle AXYZ is reflected over the line y = x. 5 3 X 2- -6 -5 -4 -3 -2 -1 |0 1 2 3 4 5 6 -t -2 -3 -4 -5 -6 What are the coordinates of the vertex of the right angle in AX'Y'Z'?

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: Determine the point(s) on y=x2-1 that are closest the point (7,7)

A: Let (x, y) be the point on the given graph which is closest to (7, 7). Therefore the distance…

Q: Perpendicular to the line y=−1/2x+1 containing the point (3,6)

A: Solution is done in step 2

Q: 6. Find the symmetric equation of the line parallel to ở = (1,4, 6) + t(−2, 4, 7) that intersects…

A: Given problem:- 6. Find the symmetric equation of the line parallel to r = (1,4,6) + t(−2, 4, 7)…

Q: Find the point on the line 5x + y = 5 that is closest to the point  (−4, 1).   x,y= (  , )

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Q: Drag the triangle so that it is reflected over the y-axis 10 -5- -10 -5 10 -5- -10

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Q: What are the coordinates of (-4, 1) after a reflection over the y-axis? 10- 8- 6+ 4+ (-6, 1) (-4, 1)…

A: Given, The coordinates of point -4, 1  We have to find the coordinates of point -4, 1 after a…

Q: Find the angle between the lines x+3y-1=0 and 2x+3y-5=0

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Q: Two cars are traveling on two different roads that are perpendicular to each other. On a coordinate…

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Q: What is the distance between points (-6, -9) and (3, 3) on the coordinate plane? 8- 7- 6- 4- 3- 1…

A: Solve using co-ordinate geometry

Q: 2. Find the exact value of the distance between the line of intersection of the planes 2x - y + 2z =…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the point on y – axis which is equidistant from the points (3, 1, 2) and (5, 5, 2)

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Q: An object is traveling along a path described by y = x + 3. Where along that path will the object be…

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Q: Find the points on the cone 2² = x² + y² that are closest to the point (3,-3,0)

A: Cone Equation: z2=x2+y2 Given point: 3,-3,0 To find: the points on the cone nearest to the given…

Q: 3. Mayor Moreno issued a 24-hour lockdown in one of the barangays in Manila. A 24-hour lockdown will…

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Q: Find the coordinates of the image of the point (-22) when it is reflected across the line y-7 O…

A: Given that the line y=7 and the coordinates whose image has to be found is (-2,2) Let A be the…

Q: Find the point on the line 6x + y = 6 that is closest to the point (-4, 1). (x, y) = %3D

A: We have to find a point on the line 6x + y = 6 that is closest to the point (-4,1). Concept Used -…

Q: 8) Determine an equation of a line that passes through the point P (5,-2,3) and is parallel to the…

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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: Find the angle between the lines y-V3x-5=0 and 3y-x+6=0. %3D

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Q: Find the length of the curve y=x^5/6+1/10x^3, 2<x<4

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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: 3. Line segment JK in the xy-coordinate plane has endpoints with coordinates (-4, 11) and (8, -1).…

A: As per guidelines we can answer only one question at a time, so the first question can be answered…

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

A: Given : Point : 1,-2, 4 Plane : 3x+2y+6z = 5

Q: XIV. Give equation of straight line through point (1,3,-2) perpendicular to z = Зх-2y +4.

A: Given z=3x−2y+4 and point is x0,y0,z0=1,3,−2 We have to find the equation of straight line through…

Q: Sketch the translation of the triangle with the rule (x, y) → (x+5, y+1). T 5- -10 -5 10 -5- 5

A: The coordinates of vertices of the blue triangle (1st quadrant) are A1, 1, B3, 1 and C3, 5. Now, Use…

Q: Find the distance from the point to the line.   (−4,4,−1)​; x=-3+3t, y=-1+t, z=1+2t   The distance…

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Q: A Find the Distance from the point (2,-6) to the line 3x+ 4y t6=0 B Find the distance between the…

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Q: roblem 4.1 Find the point on the line y = 2x + 3 that is closest to the origin.

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Q: Find the distance from the point (-6,2,-7) to the plane -x + 4y = 2z = 22.

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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: The line through the point (0, 14, – 10) and parallel to the line x= -1 + 21, y = 6 – 31, z = 3 + 9t…

A: If the line is parallel to the line x = -1 + 2t; y=6 -3t and z=3 + 9t, then the line is parallel to…

Q: Find the coordinates of the image of the point (-2, 2) when it is reflected across the line y-7 O(2…

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Q: The coordinates of a point on the line x+ y+1 = 0 which is at a distance /2 units from the line 3x +…

A: Given: The line x+y+1=0 which is at a distance 2 units from the line 3x+4y-2=0 To find: Coordinates…

Q: 29. (-2, 2) reflected through the y-axis is a. (-2, 2) b. (2, 2) с. (-2, -2) d. (2, -2)

A: Rule:-  A point ( x,y ) After reflection through y axis becomes ( -x , y)

Q: 3. Through the point (4, -5, 20) and perpendicular to the plane x + 3y – 6z - 8 = 0.

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Q: Calculate the distance between the points P = (-7, 6) and N=(-2, 2) in the coordinate plane. Give an…

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Q: Find the distance between (2,0) and (8, - 3) The distance d between the points

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Q: Find the distance from the point (-2, 2, 3) to the plane -3x + y – z = 9.

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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: point

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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: 6. Find the distance between the point (-3, 1) and the line 4x + 3y + 4 = 0.

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Q: Find all points on the y-axis that are 5 units from the point (4, 4).

A: Distance between two points (x1,y1) and (x2,y2) on the graph is given by the distance formula, that…

Q: nd the distance between the points (-3,0) and (2,5)

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Q: An object is traveling along a path described by y =x +3. Where along that path will the object be…

A: Given: An object is travelling along a path described by y=x+3.

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

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Q: Find the angle between the lines y-V3x-5=0 and 3y-x+6=0.

A: Introduction :

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.