The coordinates of a point in the xy-coordinate system are given. Assuming that the XY-axes are found by rotating the xy-axes counterclockwise by an angle 0 (which means a point would rotate clockwise by that angle), find the corresponding

Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

A: Given: Points.P=(0,4,-1)A=(4,3,4)B=(-2,2,1)

Q: Determine the are of a triangle formed by the given 7x+8y=69 and the coordinate axes x and y.

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Q: 1. give the equivalent cartesian coordinates of ρ = π

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Q: Find all points having an x-coordinate of 3 whose distance from the point (-2,1)is 13 (a) By using…

A: (a) By using the Pythagorean Theorem (see graph below)   Let (-2,1) denote the coordinates of the…

Q: Find the equation of the perpendicular bisector of side of the triangle having vertices…

A: Slope of a line passing through two points x1,y1,x2,y2 is given by Y2-x1x2-x1 Midpoint of two points…

Q: A, B, and C are collinear points: B is between A and C.  If AB = 3x + 4, BC = 4x - 1, and AC = 6x…

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Q: Graph the Image of polnts A and B after a reflection over the x-axis. UNI CLICK TO SELECT 10 POINT A…

A: The reflection of a point say A(x,y) over axis leads to the  new co-ordinates as A'(x,-y)  The x…

Q: Show that the points A(1, 1 + d), B(3, 3 + d), and C(6, 6 + d) are collinear (lie along a straight…

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Q: A, B, and C are collinear points: B is between A and C.  If AB = 12, BC = 18, and AC = 3x, find x.

A: If A, B, and C are collinear points and B is Between A and C, then AB + BC = AC

Q: When the axes are rotated through an angle 4 π , find the transformed equation of 3x2 + 10xy + 3y2 =…

A: Axes are rotated through an angle 4π given equation is                             3x2+10xy+3y2=9…

Q: If quadrilateral ABCD was rotated 270 degrees counterclockwise about point D, what would be the…

A: Use coni method to find the rotation of point B after 270 degree rotation, zB'-zDzB-zD=cosθ+isinθ…

Q: b. If you rotate (turn) AABC (the original) 270° counterclockwise about the origin to create AA" B"…

A: For rotation of 270 degrees counter clockwise about the origin we use the formula (x,y)→(y,−x)  That…

Q: Think of a parallelogram made with cardboard strips and hinged at each vertex so that the measure of…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: In the figure attached, find XW if yw bisects <XYZ and XY = 9, YZ = 12 and XZ = 10.

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Q: Find the component form of v if = 2 and the angle it makes with the x-axis is 60°.

A: Component of a vector v is given by vx=vcosθ      and vy=vsinθ ,  where θ is the angle made with the…

Q: Find the Cartesian coordinates of the given point. O 1) (0, 1) 2) (1, 0) 3) (0, -1) 4) (-1, 0)

A: We need to find cartesian coordinates.

Q: A power cable is to be fitted under a road and can be represented on 3D Cartesian axes as below,…

A: a. The points are A0,-40, 0 and B (40, 0,-20) Obtain the distance AB:…

Q: Write the coordinates of the vertices after a rotation 270 counterclockwise around the ori G. 6. 4.…

A: NOTE: Refresh your page if you can't see any equations. . now, if you rotate the point (x,y) 270…

Q: Let P, Q, and R be the points at 1 on the x-axis, 2 on the y-axis, and 3 on the z-axis,…

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Q: A, B, and C are collinear points: Cis the midpoint of AB. If AC = x + 11 and CB = 2x - 5, find AC.

A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the…

Q: A power cable is to be fitted under a road and can be represented on 3D Cartesian axes as below,…

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Q: Given the coordinate of one endpoint of AB and its midpoint M, find the coordinates of the other…

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Q: Find the distance from (-5,9, –12) to each of the following: 1. The xy-plane. Answer:

A: Given point :-  (-5,9,-12) To find:- Distance of given point to plane xy

Q: The coordinates of a point in the xy-coordinate system are given. Assuming that the XY-axes are…

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Q: Find the Cartesian equation of the locus of points satisfying PA + PB = 12, where A is the point…

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Q: 1. In a rectangular coordinate system, the point where the x- and y-axes meet is called the

A: Consider the provided information, In a rectangle coordinate system, the point where the x and y…

Q: Given the coordinate of one endpoint of AB and its midpoint M, find the coordinates of the other…

A: introduction:-let A and B are the endpoint of line segment AB whose cordinate (x1y1) and x2y2…

Q: 57 Find the rectangular coordinates for the point given in poloar coordinates: [4,

A: We have to find the rectangular  coordinates of the given polar coordinates of a point.

Q: Suppose S(5, 4) was rotated 270 counterclockwise about the origin, then reflected across the line x…

A: Given query is to find the the x cordinate of S''.

Q: The equation, with a restriction on x, is the terminal side of an angle 0 in standard position. 4x +…

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Q: determine the points that are symmetric with respect to (a) the x axis, (b) the y axis, and (c) the…

A: (a) Consider the point (-3, 1). Recall that to find the point that is symmetric about the x-axis, we…

Q: Calculate the latitude and longitude angles for the following Cartesian coordinates.…

A: To calculate the latitude and longitude angles of given Cartesian coordinates. For first coordinate…

Q: 4- Find the direction and direction from the point (1, 3) for which the values off do not change,…

A: 4)Given isfx,y=e2y arc tan3y3x at point 1,3A function  fx,y has no change in any direction that is…

Q: Find the coordinates of the image. Ry-axis (S)

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Q: Consider point W on the coordinate plane y 51 w/ 1.

A: Here if we are going through x-axis. Then it will give points 3 and -4. Because x-axis value will…

Q: In parallelogram WXYZ, diagonals WY and XZ intersect at point A. Give WA = x^2 - 48 and AY = x^2 -…

A: We have to find WY

Q: when the axes are rotated through an angle x/4,find the transformed equation of 3x2+10xy+3y2=9

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Q: Find x such that the points A(x, 5), B(2, 3), and C(4, - 5) are collinear.

A: Given. A(x,5), B(2,3) and C(4,-5) are collinear.

Q: When the axes are rotated through an angle x/4,Find the transformed equation of 3x2+10xy+3y2=9

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Q: Graph the image of parallelogram BCDE after a rotation 270° counterclockwise around the origin. 10…

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Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

A:

Q: Solve for the orthogonal traectories y = x2- cX

A: The orthogonal trajectory is a curve that intersects each of the family's curves at a right angle.…

Q: The equation, with a restriction on x, is the terminal side of an angle 0 in standard position. 3x…

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Q: A point moves so that the ratio of its distances from 3x + 4y + 8 = 0 and 4x + 3y – 6 = 0 is 2. Find…

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Q: A paritcle is at the point P1 (3,7) and is displaced to the point P2 (x,y) , where d= 10m and the…

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Q: An angle in a rectangular coordinate system is in standard position if its vertex is at the________…

A: To fill in the given blanks.

Q: 9. Determine the indices for the directions shown in tl D 112

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Q: Graph the image of square TUVW after a reflection across the y-axis. 10 6- 4. W V -10 -4 0. 4. 10 -4…

A: Draw a schematic diagram of given figure. .

Q: On a dark night, two ships, Saga and Hero, sail parallel to a straight coastline on which there are…

A: We have, I=1b2+x+82+1b2+x-82dIdx=-2x+8b2+x+822+-2x-8b2+x-822     =-2x-8b2+x+822+-2x+8b2+x-822…

Q: Given that z1 = 1+i, z2 = 2+ 6i and z3 = -1+7i, find the three possible values of z4 so that the…

A: Given that z1=1+iz2=2+6iz3=-1+7i We need to find three possible values of z4 such that z1,z2,z3,z4…

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.