Let P be the parallelogram in the plane with vertices (0,0), (1,2), (1, 1), and (2, 3). Find SSp¤ dA. (The easiest way is to use a change of variables which turns P into a square.)

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: Find a plane through the points (1,-6,1), (-5,-2,3), (-4,5,-4). Write your answer in the form Ax +…

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Q: Describe a method for determining whether four points P, Q , R , and S lie in the same plane?

A: We will show a method for determining whether four points P,Q,R and S lie in the same plane.

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: The parallelogram (ABCD) has vertices at A(2, -1, 4), B(1,0,-1), C(1,2,3), and D, then اخترأحد…

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Q: If two vertices of an equilateral triangle are at (0, 0) and (2a, 0), what point is the third…

A: The given diagram is, Since, ∆ABC is equilateral triangle. AB=BC=AC. ⇒AB2=BC2=AC2 Suppose point A…

Q: Find the distance between the plane P:8x+3y+9%= 0 and the point (1,-5,20)

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Q: Use slopes to show that the quadrilateral with vertices at (1, 3), (-5/2, 2), (-7/2, 4), and (2, 1)…

A: Given that Vertices of quadrilateral are A1, 3, B-72, 4, C-52, 2 and D2, 1   It is known that the…

Q: Find the equation of the perpendicular bisector of the segment joining (1, 2) and (5, 4)

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Q: Line AB is formed by the vertices A (1, 2, -2) and B (-1, 0, 2). If C is the midpoint of AB, find…

A: Given,  the coordinates of A and B which forms line AB  And c is the mid point is AB Hence the…

Q: Determine if the points X(26, 24), Y(2, 22), and Z(0, 5) form the vertices of a right triangle.

A: Given points are X26,24, Y2,22 and Z0,5. To determine whether points form the vertices of a right…

Q: Use v=<3/5,4/5>,w=<-4/5, 3/5>, to verify the Parallelogram Law

A: The given vectors are

Q: (b) Find the area of a triangle with the points A(1,0, 0), B(0,1,0), C(0,0, 1) as it vertices by…

A: (b) We have to find area of triangle with the points A1,0,0 , B0,1,0 and C0,0,1 by using cross…

Q: 3. A(-5, 8), B(-2, 14), C(12, 7), D(9, 1)

A: As per guideline we have to solve only one

Q: Determine the coordinates for the intersection of the diagonals in RSTU with vertices at…

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Q: 1. Rhombus ABCD with vertices A(-3, -2), B(0, 3), C(5, 6), and D(2, 1): (x, y)- (x+2, y-6)

A: In Rhombus, A=(-3,-2)B=(0,3)C=(5,6)D=(2,1)

Q: 14) Write the equation of the perpendicular bisector of segment QR if Q(3, -2) and R(7, 6)

A: Find the equation

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

A: The triangle has vertices A (-1,-3),B(5,-3) and C(5,5) so to find the perpendicular bisectors let D,…

Q: and the coordinate planes.

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Q: Decide whether each parallelogram JKLM is a rectangle, a rhombus, or a square. Give ALL names that…

A: Decide whether each parallelogram JKLM is a rectangle, a rhombus, or a square. Give ALL names that…

Q: Find the coordinates of the intersection of the diagonals or Parallelogram PRYZ with given vertices.…

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Q: A parallelogram has point symmetry about the point where its two diagonals intersect.

A: Given query is to find that given statement is true or false.

Q: The coordinates of the vertices of a rectangle WIND are W(-2, 6), I(10, 6), N(10, -3), and D(-2,…

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Q: Sketch the rectangle in the coordinate plane whose vertices are (3, 5), (5, 5), (3, 1), and (5, 1).…

A: We know that,  Area of rectangle = length * Width Perimeter of rectangle = 2(length + width)

Q: ectors to decide whether the triangle with vertices P(1,-3,-2), Q(2,0,-4), R(6,-2,-5), and is…

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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: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(5, -2,…

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Q: Let R be the interior of the parallelogram with vertices (-3, 1), (-1,0), (–1,2), and (1, 1).…

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Q: Calculate , (7xy+ 3e²) dS, where S is the triangle with vertices (0,0, 3), (1,0, 2), and (0, 4, 1).…

A: Given vertices of triangle are 0,0,3 ,1,0,2 ,0,4,1 Let the equation of plane through these points…

Q: (c) Consider the parallelepiped with sides: u=(5,-2,1), v=(3, 2, 4), and w=(-6,1,1). V

A: Angle between two vector V and W found using cosine function

Q: The midpoint of AB is M(2, –2). If the coordinates of A are (-2, 1), what are the coordinates of B?

A: Recall: Mid point Formula: The midpoint of M(x,y) of the line segment from A(x1,y1) to B(x2,y2) is…

Q: Verify that parallelogram ABCD with vertices A(-5, – 1), B(-9, 6), C(-1, 5), and D(3, – 2) is a…

A: We can verify this as below using the diagonals.

Q: Use the diagonals to determine whether the parallelogram with the given vertices is a rectangle,…

A: Given: P(-5, 2)Q(4, 5)R(6, -1)S(-3, -4)

Q: Draw an image of quadrilateral ABCD on the coordinate plane reflected over the y-axis

A: when Quralatral reflected over y-axis then y coordinate does not change only x coordinate change

Q: Find the equation of the plane which contains the line ( 2 + t , 3 − t , 4 + 2 t )and the point ( 0…

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Q: a). Determine a pair of planes whose intersection is the given line. = 2-3k, y = 3+e , Z- 2 -4€

A: Note: as per our guidelines we are supposed to answer only one question.* *Kindly repost other…

Q: Which of the points A(-4,0,–1), B(3,1,–5), and C(2,4, 6) is closest to the yz-plan Which point lies…

A: Given: A(-4,0,-1)  B(3,1,-5)  and C(2,4,6) To find: Which is closet to the yz plane Which is lies on…

Q: Determine the coordinates for the intersection of the diagonals in RSTU with vertices at…

A:

Q: Consider the parallelogram with vertices at (0,0), (4, 0), (2, 3), and (6, 3). Where do the…

A: Diagonal of parallelogram bisects each other

Q: ABCD is a rhombus with sides AB and BC. If AB : %3D 12x - 2 and BC = 3x + 7. Find CD. CD =

A: In rhombus ABCD, AB = 12x-2 BC = 3x+7 To evaluate : The side length CD

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: Determine whether the planes are parallel, perpendicular, or neither. 7x + 7y + 7z = 1, 7x – 7y + 7z…

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Q: Determine whether the points P(1, −2, 3), Q(2, 1, 0), and R(4, 7, −6)                    are…

A: Given, The points P(1, −2, 3), Q(2, 1, 0), and R(4, 7, −6).

Q: Show whether or not the diagonals of parallelogram ABCD bisect each other given A(-2,2), B(1,4),…

A: The vertices of the parallelogram are given  A(-2, 2) B(1, 4) C(2, 8) D(-1, 6)

Q: Show that A(-4, – 1), B(0, –2), C(6, 1), and D(2, 2) are vertices of a parallelogram.

A: Given  A(-4,-1), B(0,-2), C(6,1) and D(2,2) To show: ABCD are vertices of a parallelogram.

Q: hat are the coordinates of the point on the directed line segment from (–7,5) t ',-9) that…

A: In the question we need to find the coordinates of a point which divides the line segment joining…

Q: Find the distance between the parallel planes P and P P: 2z -y+ 3z -6 =0 P: 4z - 2y + 6z - 2 =0

A: Distance between the parallel planes ax+by+cz+d1=0 and ax+by+cz+d2=0 is…

Q: Graph the first-octant portion of each plane. 4x + 2y + 3z = 24

A: We have to find the graph the first-octant of the plane. To find x- intercept of the plane put y=0…

Q: P, Q and How far is the point S from the plane that contains the points R?

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…