 7.1: In the figure, which of the points A, B, C, D, and E belong to the ...
 7.2: In the figure, which of the points F, G, H, J, and K belong to the ...
 7.3: In Exercises 3 to 8, use the drawing provided. Given: Obtuse Constr...
 7.4: In Exercises 3 to 8, use the drawing provided. Given: Obtuse Constr...
 7.5: In Exercises 3 to 8, use the drawing provided. Given: Obtuse Constr...
 7.6: In Exercises 3 to 8, use the drawing provided. Given: Obtuse Constr...
 7.7: In Exercises 3 to 8, use the drawing provided. Given: Obtuse Constr...
 7.8: In Exercises 3 to 8, use the drawing provided. Given: Obtuse Constr...
 7.9: Given: Right Construct: The median from S to
 7.10: Given: Right Construct: The median from R to
 7.11: In Exercises 11 to 22, sketch and describe each locus in the plane....
 7.12: In Exercises 11 to 22, sketch and describe each locus in the plane....
 7.13: In Exercises 11 to 22, sketch and describe each locus in the plane....
 7.14: In Exercises 11 to 22, sketch and describe each locus in the plane....
 7.15: In Exercises 11 to 22, sketch and describe each locus in the plane....
 7.16: In Exercises 11 to 22, sketch and describe each locus in the plane....
 7.17: In Exercises 11 to 22, sketch and describe each locus in the plane....
 7.18: In Exercises 11 to 22, sketch and describe each locus in the plane....
 7.19: In Exercises 11 to 22, sketch and describe each locus in the plane....
 7.20: In Exercises 11 to 22, sketch and describe each locus in the plane....
 7.21: In Exercises 11 to 22, sketch and describe each locus in the plane....
 7.22: In Exercises 11 to 22, sketch and describe each locus in the plane....
 7.23: For Exercises 21 to 26, use the grid and your compass (as needed) t...
 7.24: For Exercises 21 to 26, use the grid and your compass (as needed) t...
 7.25: For Exercises 21 to 26, use the grid and your compass (as needed) t...
 7.26: For Exercises 21 to 26, use the grid and your compass (as needed) t...
 7.27: In Exercises 27 to 34, sketch and describe the locus of points in s...
 7.28: In Exercises 27 to 34, sketch and describe the locus of points in s...
 7.29: In Exercises 27 to 34, sketch and describe the locus of points in s...
 7.30: In Exercises 27 to 34, sketch and describe the locus of points in s...
 7.31: In Exercises 27 to 34, sketch and describe the locus of points in s...
 7.32: In Exercises 27 to 34, sketch and describe the locus of points in s...
 7.33: In Exercises 27 to 34, sketch and describe the locus of points in s...
 7.34: In Exercises 27 to 34, sketch and describe the locus of points in s...
 7.35: In Exercises 35 and 36, use the method of proof of Theorem 7.1.1 to...
 7.36: In Exercises 35 and 36, use the method of proof of Theorem 7.1.1 to...
 7.37: In Exercises 37 to 40, refer to the line segments shown. Construct ...
 7.38: In Exercises 37 to 40, refer to the line segments shown. Construct ...
 7.39: In Exercises 37 to 40, refer to the line segments shown. Construct ...
 7.40: In Exercises 37 to 40, refer to the line segments shown. Construct ...
 7.41: Construct the three angle bisectors and then the inscribed circle f...
 7.42: Construct the three perpendicular bisectors of sides and then the c...
 7.43: Use the following theorem to locate the center of the circle of whi...
 7.44: Use the following theorem to construct the geometric mean of the nu...
 7.45: Use the following theorem to construct a triangle similar to the gi...
 7.46: Verify this locus theorem: The locus of points equidistant from two...
Solutions for Chapter 7: Locus and Concurrence
Full solutions for Elementary Geometry for College Students  6th Edition
ISBN: 9781285195698
Solutions for Chapter 7: Locus and Concurrence
Get Full SolutionsElementary Geometry for College Students was written by Patricia and is associated to the ISBN: 9781285195698. Chapter 7: Locus and Concurrence includes 46 full stepbystep solutions. Since 46 problems in chapter 7: Locus and Concurrence have been answered, more than 1480 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Elementary Geometry for College Students, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Column space C (A) =
space of all combinations of the columns of A.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Solvable system Ax = b.
The right side b is in the column space of A.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.
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