What do I do after substituting the expressions for x and y from the rotation formulas into the given equation?

Q: Q17:- In polar coordinates prove that** 第。

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Q: Find the image of (2, -2) obtained by translating 2 units up, followed by a rotation of 90°…

A: Given point is : 2,-2 To find image of 2,-2 obtained by translating 2 units up, followed by a…

Q: Consider the conic section given by the polar equation 4 1-sin 0 r=

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Q: Which Image shows a rotation?

A: Given that:  1.                                          2.

Q: Complete the following: 1. What is the difference between a rotation in two dimensions and a…

A: (1) If we consider the spherical coordinates r,θ and ϕ if the rotation is only in two dimensions…

Q: When the 2-dimensional shape shown below is rotated about the axis indicated by the dashed line, a…

A: When a 2 dimensional shape is rotated about an axis, a 3 dimensional shape is formed

Q: 9- Give five examples about application of polar coordinates in real life

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Q: 12. What will be the coordinates of point A after a 90 clockwise rotation about the origin?

A: Given coordinates of A A ( 2, -3 ) for 90 degree clockwise rotation  (x,y)→(y,-x)

Q: Express y=x^2 in polar coordinates.

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Q: Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.

A: Definition used -                                Ax2+Bxy+Cy2+Dx+Ey+F=0 , B≠0…

Q: If there is a 60° angle from the positive x-axis to the positive x′-axis, explain how to obtain the…

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Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

A: Given equation is 16x2+8xy+8y2-13=0 Angle of rotation is ϕ to eliminate the xy term. The new…

Q: Which polar coordinates represent the same point as (4, –1/2)? (Select all that apply.) (4, –5x/2)…

A: Polar coordinate

Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

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Q: Suppose that A and B are rotations of 180° about the points a and b,respectively. What is A followed…

A: Let Let A be the rotation of 180 degree about point a. Then a is midpoint of P and f(P). It follows…

Q: What is the smallest rotation clockwise about the center of the figure that will carry the entire…

A: Given figure: The main objective is to find the smallest rotation clockwise about the center of the…

Q: 4 -8 -6 -4 -2 2 4 8 10 E,

A: Given query is to find the image points after 180° counter clockwise rotation.

Q: Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.

A: If x and y axis are rotated  through an angle θ , the coordinates (x, y) of a point P relative to…

Q: Determine the coordinate of a 3D point (100.0, 29.0, -79.5) after rotating 60° across Y-axis, given…

A: Given:                       point: A100.0,29.0,-79.5                Rotation: θ = 60° across…

Q: The point (3, 4) is plotted on the coordinate plane below.   What are the coordinates of the…

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Q: Graph the image of the figure using the transfor and its image. 1) rotation 180° about the origin…

A: In the question it is asked to calculate the image of the given graph by taking a rotation of 180°,…

Q: (2) Can the change of cartesian coordinates to polar coordinates in R? be expressed as a linear…

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Q: Which figure shows a rotation followed by a translation?

A: as we can see here flag is rotated 90 degrees in a clockwise direction so here we have a rotation…

Q: When a polar function is symmetrical about both the x- and y-axes, why is it also symmetric about…

A: Given that the polar function.

Q: Determine the coordinates of the new point after a rotation of 110 about (0, 0) from the point (4,…

A: We will use  rotation matrix about origin to find new point  If after rotating through an angle θin…

Q: 6. Find the image equation of the line -2x +y + 3 = 0 under the rotation about C = (1, 1) at an…

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Q: Find parametric equations for the line segment starting at P(3, –4) and ending at Q(-5,2).

A: We have to find the parametric equation of the given line.

Q: Transform (0, y) from rectangular into polar form (here y is any negative number).

A: We have convert rectangular coordinates (0 , y) into polar coordinates: Where y is negative number-

Q: Give each rule for counterclockwise rotation about the origin 180°: (x,y)

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Q: How does an image compare to its preimage after a -45 degree rotation?

A: Query- How does an image compare to its preimage after a -45 degree rotation. Answer-As reflection…

Q: ン Plot the point whose polar coordinates are 4, 5+ 4 2 -5 -4 -3 -2 -1 4 5 -1 -2 -3 3.

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Q: [] when 0 = 180° and explain what happens to the point (x, y) when this rotation is applied. 2.2…

A: Given M×xy and θ=180°

Q: How do you convert x2+y2 = 16x2-4y2 to a polar equation?

A: THE EXPLANATION HAS BEEN GIVEN IN  THE ATTACHED FILE.

Q: 1) reflection are equivalent to a rotation. True or False: Three consecutive reflections across…

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

Q: coordinates of A(-11.5, 9), B(14, 8), and C(6, -7). What are the coordinates of its image after a…

A: Given data:     The first point is: A=(x1,y1)=(-11.5,9). The second point is: B=(x2,y2)=(14,8). The…

Q: If the original 2-D shape and the reflected image combine to form a new 2-D shape, what is the angle…

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Q: What is the image equation of the line 2x+y-1=O under the rotation about the point (1, -1) at an…

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Q: 10. What will be the coordinates of point T after a 180* rotation about the origin?

A: Given coordinates of RSTU R (2,5) S (7,7) T (6,4) U (1,2)

Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

A:

Q: What is the smallest rotation clockwise about the center of the figure that will carry the entire…

A: Given figure: The main objective is to find the smallest rotation clockwise about the center of the…

Q: When the 2-dimensional shape shown below is rotated about the axis indicated by the dashed line, a…

A: Given shape: A triangle

Q: What are the coordinates of A 'after a 180 ° clockwise rotation?

A: Rotation of 180 degrees clockwise means rotation about the origin.

Q: Find a set of parametric equations for the line segment from (-1,5) to (9,–4).

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Q: Let f1 be reflection with respect to the y-axis and let f2 be counterclockwise rotation through π/2…

A: Given:  f1 be reflection with respect to the y-axis and let f2 be counterclockwise rotation through…

Q: What is the rotation that translates AWXY to ΔW 'ΧΎ'?

A: W'X' Side of W'X'Y' triangle is Perpendicular to WX side of WXY Triangle.

Q: The rotation about the origin at an angle e=180° is defined by (ху)-(ху) (ху)-(ух) O (x.y)->(x,-y)…

A: The rotation about the origin at an angle 180° is defined by :-

Q: What is the image of (-2,2) under the rotation about the origin at an angle e=180°? O (2,-2) (-2,2)…

A: Given that