In Exercises 17 and 18, for the triangle with the given vertices A, B , C, find the lengths of its sides, and deter- mine which of its angles are acute, obtuse, or right angles. 17/  A=(2,-3,6),B=(I,3,-2),C=(1,7,1)

Q: Consider the triangle with vertices in the points D(-5,0,5), E(2, 1,3), and C(3, 1,4). Compute the…

A: Vertices of triangle D(-5, 0,5) , E(2, 1,3) and C(3, 1,4) . We have to compute the area of triangle…

Q: Find the point R that breaks the directed segment Pe in a ratio of 1:3, given point P(-4,5) and…

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Q: If AB = –7i + 3j + 8k and A is the point (-2, –3, 6), find B. %3D

A: Consider the given vector as AB→=-7i+3j+8k and point A-2,-3,6

Q: in the coordinate plane, quadrilateral ABCD has vertices A(-2,3), B(4,5), C(10,-1), and D(8,-9). Let…

A: In the coordinate plane, quadrilateral ABCD has vertices A(-2,3), B(4,5), C(10,-1), and D(8,-9). Let…

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(8, 7,…

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Q: Find the measures of the angles of the triangle whose vertices are A(1,0), B(2,1), and C(1,-2). 4.

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Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(8, -2,…

A: FIND THE AREA

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: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(-1, 6,…

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Q: Show that the quadrilateral with the given vertices is a trapezoid. Then decide whether it is…

A: Find if the figure is an isosceles trapezoid and find all the 4 slopes.

Q: Let A=(1,2,3), B=(3,4,3), C=(1,4,4) and D=(2,2,5) vertices of a parallelepiped in space and suppose…

A: Given, ABCD are the vertices of a parallelepiped.  B, C, D are adjacent to A.  To find:  The…

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: In Exercises 3 and 4, list the sides of the given triangle from shortest to longest. 4. B115° 52° D

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Q: Given parallelogram ABCD with vertices A(-3,1), B (2,6), C(9,5) and D(4,0) PROVE ABCD is a rhombus.

A: Given that: ABCD is a parallelogram with vertices A(-3,1), B (2,6), C(9,5) and D(4,0).

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(-2, -6,…

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Q: 2. Determine what type of triangle does the vertices P, (1, 3) P2(4,0), and P3(-3,-7).

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Q: 3) 9ry dA, R is the triangle with vertices (0,0), (0,3) and (4, 3)

A: Given integral to evaluate ∫∫R9xydA R is triangle with vertices 0,0,0,3,4,3 The triangle will be

Q: If D is the triangle with vertices (0,0), (40,0), (40,25), then dA=

A: The triangle D is with the vertices (0,0), (40,0) & (40,25). The line passing through (0,0) and…

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: The cosine of the acute angle e between the diagonais of a quadriateral having vertices at (0,0,0),…

A: Given:

Q: Prove that ABCD with vertices 4(-1,3), B(-4,-1), C(1,-1), and D(4,3) is a rhombus assuming it is…

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Q: What are the coordinates of the point on the directed line segment from (1,-5) to (10, 1) that…

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Q: Vaughn Pang sketched trapezoid RUIZ on a coordinate plane. RUIZ has vertices located at R(1,4),…

A: Given:In trapezoid RUIZR≡1,4U≡-2,0I≡7,0Z≡3,4To find:Perimeter of RUIZ

Q: Show that the quadrilateral with the given vertices is a trapezoid. Then decide whether it is…

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Q: A quadrilateral has vertices A = (0, 0), B = (2,4), C = (0,5), and D = (-2, 1). Prove ABCD is a…

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Q: The vertices of quadrilateral KAIT are K(0,0), A(a, 0), I(a + b, c), and T(b, c). Use coordinate…

A: Parallelogram is a kind of quadrilateral with two pairs of opposite sides. In a parallelogram, the…

Q: Consider the triangle with vertices at R(- a, 0), S(a, 0), and T(0, b). Explain why ARST is an…

A: Given:

Q: Find the area of the triangle with vertices P(1, 0, 7), Q(0, 6, 7), and R(1, 4, 0).

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Q: Evaluate ry dr + r'dy, where C is the rectangle with vertices (0,0), (3,0), (3,1), and (0,1)

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Q: 6. In Exercises 7 and 8, use the following information to find the coordinates of the incenter N of…

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Q: he coordinates of the vertices of quadrilateral HIJK re H(1, 4), I(3, 2), J(-1, –4), and K(-3, -2).…

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Q: Consider a triangle with vertices X, Y, and Z.

A: Definition used -              Triangle law of vector addition -                  According to…

Q: EXERCISE 4.1 Given the three points P₁ = (10,−5, 4), P₂ = (8,−4, 3.2), and P3 = (8, 4, 3.2), derive…

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Q: 7. Find the measures of the hyperbolic angles of the Euclidean square with vertices (0, 1), (0, 2),…

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Q: 2 Prove that a quadrilateral with the vertices A(-2,3), B(2,6), C(7,6) and D(3,3) is a rhombus. IB

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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'L B'…

A: The given coordinates of rhombus is  A-3,-2, B0,3, C5,6, D2,1 The transformation is x,y→x+2,y-6 So…

Q: Find the measures of the angles of the triangle whose A. vertices are A(1,0), B(2,1), and C(1,-2).

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Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(10, -7,…

A:

Q: Find the coordinates of the orthocenter of a triangle with vertices at each set of points on a…

A: Given that: (1, 5), (6, 10), (0, 16)

Q: Consider the quadrilateral with vertices at M(0, 0), N(a, 0), P(a, b), and Q(0, b). Explain why MNPQ…

A: Given figure:

Q: Show that quadrilateral RSTV with vertices R(- 5, - 3), S(1, – 11), T(7, -6), and V(1, 2) is a…

A: Solution: Consider the given that RSTV has vertices R(-5, -3) , S(1, -11), T(7, -6), and V(1, 2)…

Q: The vertices of a quadrilateral are G(4, - 1), O(0, 0), L(2, 6), and D(6, 5). Show that…

A: Given: The vertices of a quadrilateral GOLD          G4,-1O0,0L2,6D6,5…

Q: B. Find the perimeter of the triangle whose vertices are: 1. A(2,1), B(3, -5) and C(1, -3) 2.…

A: 1. A2,1, B3,-5, C1,-32. P3,0, Q6,4, R-1,3

Q: 2. The diamond in a deck of playing cards is a rhombus. What does that mean about its diagonals?

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Q: Prove that the midpoint of the hypotenuse of any right triangle is equidistant from the vertices.…

A: To solve the given problem

Q: 3. Evaluate y dA, where D is the triangle with vertices (2,0), (1,2), and (0, 2).

A: The question is from Advanced Calculus

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

A: Given points, A(1,1,3) B(2,7,1) C(4,10,-6) D(3,4,-4) Let a,b,c,d, are position vectors of point…

Q: Find the point R that breaks the directed segment Pe in a ratio of 1:3, given point P(-4,5) and…

A: Here We will find the coordinate of the point R .

Q: A quadrilateral has vertices A = (0, 0), B= (2,4), C = (0,5), and D = (-2, 1). Prove ABCD is a…

A: Given :

Q: Justin sketched trapezoid BALI on a coordinate plane. BALI has vertices located at B(1,4), A(-2,0),…

A: