Let C denote the rectangle with vertices (0,-2), (0, 2), (2,-2), and (2, 2), oriented counterclockwise. Find So COS TTZ 2²-1 dz

Q: 60. Show that the distance between two points P1(x1, y1) and P2(x2, y2) is invariant under rotation.…

A: For the points P1 and P2 , the distance between the points is given d(P1,P2)=(x2-x1)2+y2-y12 . For a…

Q: Q.2)(A) Find a formula for the area of the triangle in the xy-plane with vertices at A(0, 0), B(a1,…

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Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

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Q: Let P = (0,0, 0), Q = (1, –1, –2), R = (2,1, 1). Find the area of the triangle PQR. area = Let T =…

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Q: K' is the image of the point K after a reflection. K(2, -6) → K'(-2, -6) Over which axis was point K…

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Q: Transform triangle ABC with vertices A (4,0), B(0, 2), and C(-2, -1) as shown. RO. 1800(ABC) A'. В'…

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Q: fy the notation that shows the transformation of triangle SML onto triangle S'M'L' to show the…

A: Explanation and solutions is given below....

Q: 1 (x-3)² y² + 289 64 Center: Vertices: Foci: Directrices: 1 Co-Vertices:

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Q: 20b. Find the coordinates of A' after A(-3, 4) has been reflected: Reflection in the x-axis: A'= I…

A: To find the reflections

Q: Give the coordinates of the harmonic conjugate of (–1, –1, 0) with respect to (1, 1, 1) and (3, 3,…

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Q: 5. Find the image of the triangle ABC, A(4,-1), B(1,0), C(3,1) under reflection 4y = 3x + 5 followed…

A: To find the image of the triangles ABC under the specified transformations, we need to follow these…

Q: Prove that for A # B, AB S AB S AB.

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Q: Find midpoint M of P,P2, which joins P1(5, -7, 2) and P2(2, 5, 6), as shown in Figure 10.46 of…

A: Formula used : Mid-point formula Mx1+x22,y1+y22,z1+z22 Here (x1,y1,z1) and (x2,y2,z2) are the end…

Q: Calculate E∫x3dx1dx2dx3, where E is the vertex tetrahedron (0, 0, 0), (1, 1, 0), (1, 0, 0),(1, 0,…

A: The solution is given as follows :

Q: -1 Find the minors and cofactor of A given by 2 -1 1

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Q: Find the cross product u x 7 where =5i +4j -2k and 7 = (-1, -7,8). uxv=

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Q: Prove that the point 2a +b-c, 5a -b+ 2c and 8a – 3b+5c are collinear.

A: Given, 3 vectors or points, A(2,1,-1) B(5,-1,2) C(8,-3,5)

Q: Imagine a triangle △ABC where A(−53,−60,−49), B(−102,−98,−107), and C(3,6,5) is in 3D space. A point…

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Q: Determine the area of AABC if A = (2, 1), B = (5, 3), and C is the reflection of B across the x…

A: Given: A triangle △ABC, with vertices are A=2,1, B=5,3, and C is the reflection of B across the…

Q: A rectangle ha verices at P (6, 6), Q (6, -6), R (-6, -6) and S (-6, 6). The origin is the center of…

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Q: Evaluate ([cos (x – y)sin(x+ y)dA, where R is the triangle with vertices (0,0), R (-1,7), and (7,7)…

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Q: Find the area of the triangle formed by the points A = (3, –1, 2), B = (1, 1, 0), and C = (1,2,–1).

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Q: Describe the loci zz−2z−2z+8 = 0 expressed in terms of conjugate coordinates z, z.

A: It is given thatzz¯-2z-2z¯+8=0Where,z¯ is the conjugate co-ordinate of z.We have describe the locus.

Q: Q2) Evaluate the ffdx dy using polar coordinate.

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Q: Use cross products to find the area of the quadrilateral in the xy-plane defined by (0, 0), (1, -1),…

A: The quadrilateral is formed by the vertices in the xy-plane defined by 0, 0, 1,-1, 3, 1, and 2, 8.…

Q: Describe the reflection of △FGH△FGH with vertices F(−3, 2), G(−4, −1)F(-3, 2), G(-4, -1), and H(−6,…

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Q: Find polar coordinates (r, 0) of the point (-2√2, 2√2), where r <0 and 0 ≤6 a. 5 *(-2√2. ST) 3 b. 2π…

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