Given the points: A(1,-2, 1), B(3,2, 2), C(-2,1,5) prove that A, Band C are the vertices of right triangle.

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: Prove that triangle ABC, which has vertices 4(3.4), B(5,-2), and C(1,-2) is isosceles. А (3,4) 4 3 2…

A: The given vertices of the triangle are  A(3, 4) B(5, - 2) C(1, - 2)

Q: If D is the triangle with vertices (0,0), (55,0), (55,49), then dA=

A: double integration

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: Prove that the points M(2, 5), N(12, 3), and O(10, 11) are the vertices of a right triangle

A: Given the points

Q: Prove that triangle ABC, which has vertices  , , and  is isosceles.

A: We are given the following triangle.             If we could show that AB=AC then we are done.

Q: I, 1,,I, I is the incentre, the excentres opposite to the vertices A,B,C of a are triangle ABC.…

A: GIVEN I is the in center , I1,I2,I3 are the ex centers opposite to to vertices A,B,C of a triangle…

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: If D is the triangle with vertices (0,0), (55,0), (55,60), then dA=

A:

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: 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: Find the area of the triangle with vertices P(1,3,–4), Q(0, 0,0) and

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

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Q: a If you moved Triangle 1 onto Triangle 2, which vertices would match?

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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: Let points A; B , C , and D in R3 have respective coordinates (1, 2, 3), (−2, 3, 5), (0, 3, 6), and…

A: Given: A(1, 2, 3), B(−2, 3, 5), C(0, 3, 6), D(3, 2, 4)

Q: Suppose that (a) points A, B, and C are collinear and (b) AB > AC. Which point can you conclude…

A: (a) A, B and C are collinear⇒ A, B and C lie on a straight line

Q: 1. Show that (2, 1, 6), (4, 7, 9) and (8, 5, -6) are the vertices of a right triangle by finding the…

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Q: Suppose that points A, B, and C are collinear and AB>AC. Which point can you conclude cannot lie…

A: Given   (a) points A,B, and C are collinear and   (b) AB > AC.

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

A: Let A(2,-1,4) , B(1,0,-1) , C( 1,2,3) and D(x,y,z) Let AC be one diagonal and BD be another…

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

A: Given:

Q: Find the area of the triangle with vertices P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

A: Triangle with vertices P1, -1, 0, Q2, 1, -1 & R-1, 1, 2.…

Q: Show that A(-3, 1), B(1, -1), C(4, 1), and D(3, 5) are vertices of a trapezoid.

A: Given vertices are A-3,1, B1,-1, C4,1 and D3,5. To show the vertices are of a trapezoid. Solution:…

Q: Show that the vertices of any rectangle are co-circular by using the converse of the Power of point…

A: Geometry

Q: Show that the points A = (3, 4), B = (1, 1), and C = ( - 2, 3) are the vertices of an isosceles…

A: Given: Points are A = (3, 4), B = (1, 1), and C = ( - 2, 3)

Q: 4 B |2 -8 -6 -4 -2 2 4 -2 -4 9- to

A: Given the directed line segment AB

Q: A, B and C are vertices of the base of an isosceles triangle ABC. A is at point (1,2), B at (4, -1)…

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Q: Find the area of the trianlge with vertices P(1,0,1), Q(-2,1,3) and R(4,2,5). Show your work. 5.

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Q: 11) Batman drew a A that have its vertices at A(1, 2), B(4, 6), and C(8, 2). Is AABC a right…

A: Vertices of a △ABC is given. A=1,2B=4,6C=8,2

Q: Show that the triangle with vertices A(0, 0), B(1, √2), andC(2, 0) is equilateral.

A: An equilateral triangle is a triangle in which all sides are equal, and consequently, all angles are…

Q: Sketch the following points in space three, A (4,5,3); B (1,7,4) and C (2,4,6). Prove that point A,…

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Q: Given the points A(5, -1) and B(-5, 3), find the coordinates of the point P on directed line segment…

A: To find a point P(x,y) on a line segment that divides it into two segments with lengths in a ratio…

Q: Which of the following is four-point geometry?

A: Axioms of Four Point geometry is given as 1.   There are exactly four distinct points 2.   Any two…

Q: In Exercises 17 and 18, for the triangle with the given vertices A, B , C, find the lengths of its…

A: for the triangle with the given vertices A, B, C, We need to find the lengths of its sides and…

Q: 2. In Figure 3.9D, consider the hexagon to be ABQCEF. What lines are now concurrent?

A: ABCDEFA is a hexagon.  The Hexagon is circumscribing a circle (the conic section).  As per…

Q: Let A, be the center of the square inscribed in acute triangle ABC with two vertice side BC (as…

A:

Q: 7. Given the points A(-3, -4) and B(2, 0), find the coordinates of the point P on directed line…

A: Here given  endpoint of the line segment Ax1, y1=-3, -4Bx2, y2=2,0 A point P on directed line…

Q: The three sides of a triangle are 5, x, and 8. Give all possible lengths x so that the triangle is…

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Q: If D is the triangle with vertices (0,0), (82,0), (82,37), then dA=

A: Solved below

Q: Given: Quadrilateral ABCD has vertices A(-5,6), B(6,6), C(8,–3), and D(-3,–3). Prove: Quadrilateral…

A: Given:           Quadrilateral ABCD with vertices A(-5, 6), B(6, 6), C(8, -3) and D(-3, -3) To…

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

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Q: 27. Show that a triangle with vertices at (3, 5), (3, 2), and (2, 5) is a right triangle.

A: If we can prove that above triangle satisfies Pythagoras theorem then we can say that above triangle…

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(7, 2,…

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

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Q: The point on the directed line segment from (2,0) to (14,12) that divides the segment in the ratio…

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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 .