Without plotting the points or drawing the figure, find the coordinates of the new vertices of the pentagon with vertices at V(3,2), W(5,10), X(6,12), Y(−0.5,1.25), Z(1,0) that has been dilated by a factor 2.

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: The intersection of the sphere (x-3)^2 + (x+2)^2 + (z-1)^2 = 49 with each of the coordinate planes…

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Q: Find the area of the triangle bounded by the lines y=x+3, y=2x-1 and y=-3x+4

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Q: Write a paragraph explaining how the distance formula giving the distance between two points (x1,…

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Q: Find all points with coordinates of the form (a, a) that are a distance 3 from P(-2, 1).

A: Given: P(-2,1) and distance is 3. To find the other coordinate point.

Q: Find all points on the y-axis that are a distance 6 from P(5,3).

A: A point on the y axis is of the form (0,k) , where k= real number. Let (0,k) is 6 units away from…

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

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

A: Given points are , (-4,9) , (-2,6), (3,-6)Let P =(-4,9)Q = 9-2,6)R = (3,-6)Hence peremeter = Length…

Q: Given the points (x,y): (2,4), (3,7), (6, 5), (9,10) find f(8) using quadratic splines method.

A: Given that the points are x,y:2,4,3,7,6,5,9,10 We have to use quadratic splines method to find the…

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,,n2, n2),B(m,,m2,m3),C(r,,r2, 13).

A: Please see the explanation below

Q: Find the point on the plane x-y+z=7 that is closest to the point (2,4,6).

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Q: Find the points on the cone 2² = x² + y² that are closest to the point (3,-3,0)

A: Cone Equation: z2=x2+y2 Given point: 3,-3,0 To find: the points on the cone nearest to the given…

Q: Find the midpoints of the legs, then the length of the median of the trapezoid with vertices C(-4,…

A: Solution: Consider the given that vertices of trapezoid is C (-4, -3), D(-1, 4), E(4, 4), and F(7,…

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

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Q: The line in R that is parallel to the y-axis and passes through the point (1, 2, 3) has equation + t…

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Q: b. Find the distance from the point (2, –2, 3) to the intersection of the planes 2x – y + 3z = 1 and…

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Q: Find the area of the triangle with vertices: Q(4,-5,-2) R(2,-3,-1) S(1,-6,1)

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Q: Find the equ. nf line through the Pont (-2,3,4) and Parallel to Planes: 2X+3y +42=5 3X + 4Y+52=6…

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Q: What are the coordinates of the vertices of AA'B'C' after a reflection across a line through point P…

A: Given, ∆A'B'C' is formed after a reflection across a line through point P followed by a translation…

Q: Find all points on the y-axis that are a distance 13 from P(12, 6).

A: To find: All the points on y-axis that are a distance 13 from P12,6. Concept used: The x-coordinates…

Q: Find the perimeter of a triangle with vertices S(4, 5), T(-2, -3), and W(5, - 4).

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Q: 1)calculate xy dady Where D is a triangle with vertices (0,0), (5,0) and (5,5) tip:Don't use the…

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Q: Find the shortest distance between the point Q(2, 0, 0) and the line segment joining the points…

A: Formula used: Distance between the point and a line is, D=PQ×uu Where u=P2-P1

Q: 4. Find the area of the parallelogram with the points A(2,5, 6), B(4,8, 10), C(11, 7, 9) and D(9,4,…

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Q: Find the area of the triangle with the points A(1, 1,5), B(3, 4,3), and C(1,5, 7) by using the cross…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the condition for the points (a,0) ,(h,k),(0,b) when ab is not equal to 0 to be collinear

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Q: Find the shortest distance from the point ( – 1, – 2, 5) to the cone z = x² + y?. Please round to…

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Q: Evaluate ||x'y dA if D is the triangle in the xy-plane with vertices at (0,0), (5,2), and (0,2).

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Q: Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N(8, 0).

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Q: Find the coordinates of the reflection without using the coordinate plane. P (4,6) over the x-axis.

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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 all points on the y-axis that are a distance 6 from P(5, 3).

A: P5, 3 is at a distance of 6 units from the y-axis

Q: Find the shortest distance between (3,4,1 ) and the plane X+y +Z = -2

A: Using distance between plane and point formula we can calculate.

Q: Find the distance from Po = (3, 9, 6) to the plane 3x + 4y – 5 = 0.

A: The given equation of plane is 3x+4y-5=0 and the point is P0=3, 9, 6. The distance between a point…

Q: Find the area of the parallelogram with adjacent sides u = (4, 3, 0) and v = (0, 3, 1).

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Q: Find the area of the parallelogram with vertices: P(0,0,0), Q(-4,-5,4), R(-4,-3,6), S(-8,-8,10). 0

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Q: Find the area of the parallelogram determined by the points P(7, - 5,5), Q(-9, -6, - 7), R(3,6, - 8)…

A: Explanation of the answer is as follows

Q: If C is the square with vertices (+1, ±1) oriented counter- clockwise, then -y dx + x dy =

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Q: Find the midpoint M of the line segment joining the points A = (6, –3) and B = (-2, 5). %3D

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Q: Find the coordinates of the point Y that lies 2. along the directed line segment from X(-1,3) to…

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Q: Find the point on the sphere  x2+y2+z2=7056 that is farthest from the point (5,−15,−2)

A: The given question has been solved in detail

Q: When the 2-D shape is completely drawn, how many points will be inside the 2-D shape?

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Q: Find the distance from the point P(-1,3,-5) to the plane through the three points Q(3, 1, -3). R(4,…

A: The points passing through the plane are: Q3, 1, -3R4, 6, -5S5, -4, -6

Q: Find the equation of a plane containing Po (1, 2, 3) and perpendicular to n = .

A: We have to find the equation of a plane containing P0 (1,2,3) and perpendicular to n = <1, -1,…

Q: 8 If the shaded square has center at C and an area of A, find C and A. 'y-axis C• (-4, 0) (0, 0)…

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Q: A rectangle has a vertex at J(2, 2), H(4, −2), and G(−2, −5). What are the coordinates of the fourth…

A: You know that the diagonals of a rectangle bisect each other.

Q: Find the area of the triangle with the given vertices. (Hint: 1lu x v|| A(0, 0, 0), B(1, 0, 3),…

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