Prove that if A-C-D, B-F-C, and A-F-G (all in the same plane) and A, B, and C are noncollinear, then G is in the interior of ZBCD. (Hint: Give a diagram to describe the points above.)

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A: The given question has been solved below.

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Q: 8 Consider the following three points: A(1, 2, -3), B(3, 5, -2) and C(m, 1,-10m). Determine m so…

A: I am attaching image so that you understand each and every step.

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Q: Points A, B, C, and D are four noncoplanar points.a. State the postulate that guarantees the…

A: Given,

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Q: Q12.Let A(6,6), B(6,2), C(3,2) be points in the plane R².The hypotenuse of AABC is: A)5 B) AB C) AC…

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Q: Let T be a projective plane. Show that there exists lines l, m in π and a point P not on l or m.

A: Given: π is a projective plane.To prove: There exists lines l, m in π and a point P not on l or m.

Q: In the study of plane geometry, certain basic statements called axioms or postulates are accepted as…

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Q: 1. Do the planes x1+x2+x3 = 1, x1+x2 = common point of intersection? If they do, find such a point.…

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Q: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

A: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

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Q: let the vertices of a triangle be A(1,4)     B (4,7)        C(7,1) Calculate its area and height

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Q: Are these points collinear? а) А(-2, 5), В(0, 2), and C(4, — 4) b) D(-1, — 1), Е(2, — 2), and F(5,…

A: (a)       A-2,5, B0,2, C4,-4      AB=-2-02+5-32      =4+4      =22BC=0-42+2--42      =16+36…

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A: a. Find p1 (2, y) and p1(5, x). What is the range of p1? To find p1​(2,y) and p1​(5,x), we use the…

Q: 1-) Determine the values of a ond b which the planes 2x -y+ 32-1=0, x+2y-2+b = 0, X+ay-6 2 +10 = 0…

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A: Since AB=4 and area of AAPB is 8,we have                 1 2×4×h=8 or h=4where h is the height of…