 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 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 2418 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.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

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

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

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.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

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