Find the coordinates of the vertices after the prism is rotated counterclockwise about the z-axis through (a)  θ=60 (b) θ=90 (c)and θ= 120  subject; linear algebra

Q: 2. (a) Show that the points (-2x, 5x), (0, 4x), (6x, x) are collinear.

A: Given that: (-2x, 5x), (0, 4x) , (6x, x)

Q: Find all values of x so that the triangle with vertices A(-3, -4, x), B(0,-4, 0), and C(-1, -3, -2)…

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Q: 1) Vertices: (6, 10), (-10, 10) Foci: (-2 + 4 V3, 10), (-2 – 4 V3, 10) 2) Vertices: (-9, 16), (-9,…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: vertices (0,0), (0, 4), and (5,0).

A:

Q: You were asked to find the perimeter of the triangle whose vertices are the specified points in the…

A: We have to find perimeter of triangle

Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: two vertices of the a  triangle ABC are (6,-2) and B(4,3) If the co-ordinates of its centroid be…

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Q: What is the vertex of y = Vx + 4+1 O (4, -1) O (4, 1) O (-4, 1) O (-4, -1)

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Q: Find the coordinates of the centroid of the triangles whose vertices are: a. (5.7), (1, -3), (-5.1);…

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Q: 2. Find the area of the triangle with vertices (0,0), (3,1) and (1,2)

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Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: 10.) An equilateral triangular prism with all edges 4V3.

A: We know that, the surface area of an equilateral prism is, 2×3a24+3a×h where a is the side of the…

Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

A: Distance formula: let us assume two points be A (x1,y1)and B (x2,y2)the distance AB is given as…

Q: 9. Square ABCD with vertices A(-7, 5), B(-4, 7), C(-2, 4), and D(-5, 2): 90° counterclockwise 10.…

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Q: Find the area of the triangle having vertices at (−2,3,1),(1,2,3) and (3,−1,2)

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Q: Find all values of x so that the triangle with vertices A(-3,-4, x), B(0, -4, 0), and C(-1,-3,-2)…

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Q: (b) Determine the area of the triangle whose vertices are (1,1.2), (-1/2,0,2.5), and (3/3,2,3/2)by…

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Q: Show that the points (−1, 0), (3, 0), (1, 2), and (1, −2) are vertices of a square.

A: Let us consider A(-1,0) , B(3,0), C(1,2) and D(1,-2) To verify ABCD as a square We need to verify if…

Q: Find the areas of the parallelograms whose vertices are given in Exercises 35–40. 35. A(1, 0), B(0,…

A: Area of parallelogram ABCD is |AB x AD|

Q: Compute the arae of the triangle with vertices (0,0) , (1,1) (-8,-7)

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Q: 3. Enlarge triangle AABC with coordinates A(-3, 1), B(5,2), and C(6,-4) by a factor of. Find the…

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Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

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Q: Find the coordinates of the vertices of the polygon after the given translation to a new position in…

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Q: 2. Triangle VWX with vertices -1, 0), W6, 8), and X(4,-3): (x, y) (x-1, y-5)

A: Given coordinates V(-1,0)W(6,8)X(4,-3)Given transformation :(x,y)→(x-1,y-5)

Q: Write the coordinates of the vertices after a reflection over the y-axis. 104 8. 9. 4. 21 -10 -8 F 4…

A: We know that The reflection of point (x, y) across the y-axis is (-x, y).

Q: In a rectangular grid with corner points (0, 0), (0, m), (n, m) and n, 0), determine the number of…

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Q: Write the coordinates of the vertices after a reflection over the line x = 3. 10 8 6. 2. -10 -8 -4…

A: Given query is to find the coordinates of the vertices after reflection over x = 3.

Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: 2. Find the equation of the plane through the points (1,–3,2), (3,0,–1), and (0,5,5).

A: The solution is given as follows

Q: The area of the triangle formed by the vertices (2, −1, −1); (1, 1, −2) and (−3, 2, −2) is:

A: NOTE: Refresh your page if you can't see any equations. . . .

Q: A quadrilateral has the following vertices given:  P1 (1, 4), P2 (3, 4), P3 (3, 6), P4 (1, 6).  The…

A: Given points are :  P1(1,4) , P2(3,4) , P3(3,6) , P4(1,6). We will first plot those points in a…

Q: The vertices of a square are located at (1,7), (5,3) (1,-1) and (-3,3). What is the approximate…

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Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

A: Vertices of triangle are A(-9 , -6) , B(-5 , 0) and C(10,-7)Perimeter of triangle ABC = Sum of all…

Q: 4) Vertices: (14, 2). (–8, 2) Foci: (3 + 4V7, 2), (3 – 4V7, 2)

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Q: Find the point of intersection of the diagonals of the rhombus with vertices (-1, 2), (3, 4), (5,…

A: We know that diagonals of rhombus are perpendicular bisector of each other. Therefore Midpoint of…

Q: Find the area of the triangle having vertices at (-2, 3, 1). (1, 2, 3), and (3,-1, 2).

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Q: Write the coordinates of the vertices after a reflection over the x-axis. 104 8. 4. -10 -8 9- -4 2,…

A: We know that The reflection of point (x, y) across the x-axis is (x, -y).

Q: Find all values of x so that the triangle with vertices A=(-2, –1, x), B=(-4, -2, –2), and C=(-2,…

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Q: Explain why the two planes P₁: =(2,5,3)+(2,-1,-3) +(1,0,-1), s,/€ R, and P',: 7=(4,4,0)…

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Q: Find the area of the parallelogram with vertices (4,2), (8, 6), (10, 9), and (14, 13).

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Q: What is the area of a parallelogram if the coordinates of its vertices are (2, 1), (8, 1), (11, 5),…

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

Q: A rectangle has vertices at the points (0,0), (6,0), (6,4), and (0,4) on a coordinate plane as…

A: NOTE: Refresh your page if you can't see any equations. . as we can see, when the figure rotated…

Q: A parallelogram has 2 vertices (1,1) and (0,7) and their diagonals intersect at the point (4,3).…

A: Given:

Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

A: Given The vertices of the triangle are (8, 2), (4, -5), (3, -8) . Perimeter definition: Perimeter is…

Q: Consider the triangular region in the plane given by the triangle (1, 6), (6, -1), and (1, -4).…

A: See attached file for a step by step explanation.

Q: 9. Square ABCD with vertices A(-7, 5). B(-4, 7), C(-2, 4). and D(-5, 2): 90° counterclockwise

A: To graph the square with given points A,B,C,D.

Q: Find the lengths of the sides of the quadrilateral STUV with vertices S(-1,4), T(2,1), U(3,-5), and…

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Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

A: The diagram of the triangle with vertices A=(2, 7), B=(5, -10), C=(1, -5) on the coordinate axes is…

Q: Find the  area of the triangle with vertices P(1,3,5) Q(-1,4,-4) and  R(1,5,4)

A: P1,3,5 Q=-1,4,-4  R1,5,4PQ=OQ-OP     =-i∧+4j∧-4k∧-i∧-3j∧-5k∧PQ=-2i∧+j∧-9k∧PR=OR-OP     =i∧…

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.