3 8 - 6.5 3.75

7 3 8 -2

4 -6 8

0 3 2 -4 -2 -1 0 5 1

2 6 1 3 5 2 4 7 8

1 -2 1 6 3 6 4 1 4

-1 3 -3 4 -2 -1 0 -5 2

GEOMETRY What is the area of ABC with A(5, 4), B(3, -4), and C(-3, -2)?

Find the area of the triangle whose vertices are located at (2, -1), (1, 2), and (-1, 0).

10 5 6 5

8 6 5 1

-9 3 7

-2 3 4 -6

-6 8 -2 5

-9 -12 0 -7

-4 5.2 1.6

- 3.2 4.1 -5.8 3.9

3 0 2 1 6 5 2 4 1

7 -2 0 3 9 0 -4 6 0

-2 4 1 7 5 0 -2 2 -1

-3 6 1 0 5 4 6 -2 2

1 -7 6 5 3 3 -4 2 -1

3 -1 8 7 6 -3 6 2 -5

1 3 8 1 9 7 1 5 4

1 -6 5 5 -7 9 2 8 -3

8 1 6 -9 5 -2 0 4 3

GEOGRAPHY Mr. Cardona is a regional sales manager for a company in Florida. Tampa, Orlando, and Ocala outline his region. If a coordinate grid in which 1 unit = 10 miles is placed over the map of Florida with Tampa at the origin, the coordinates of the three cities are (0, 0), (7, 5), and (2.5, 10). Estimate the area of his sales territory

ARCHAEOLOGY During an archaeological dig, a coordinate grid is laid over the site to identify the location of artifacts as they are excavated. Suppose three corners of a building have been unearthed at (-1, 6), (4, 5), and (-1, -2). If each square on the grid measures one square foot, estimate the area of the floor of the building, assuming that it is triangular.

GEOMETRY Find the area of a triangle whose vertices are located at (4, 1), (2, -1), and (0, 2).

GEOMETRY Find the area of the polygon shown at the right.

Solve for x if det 2 5 x -3  = 24.

Solve det 4 -x -6 x -3 2 -2 1 3  = -3 for x.

GEOMETRY Find the value of x such that the area of a triangle whose vertices have coordinates (6, 5), (8, 2), and (x, 11) is 15 square units.

GEOMETRY The area of a triangle ABC is 2 square units. The vertices of the triangle are A(-1, 5), B(3, 1), and C(-1, y). What are the possible values of y?

3 8 - 6.5 3.75 

10 40 70 20 50 80 30 60 90

10 -3 16 12 18 -2 4 -9 -1 

OPEN ENDED Write a matrix whose determinant is zero.

FIND THE ERROR Khalid and Erica are finding the determinant of 8 -5 3 2  . Who is correct? Explain your reasoning

REASONING Find a counterexample to disprove the following statement. Two different matrices can never have the same determinant.

CHALLENGE Find a third-order determinant in which no element is 0, but for which the determinant is 0.

Writing in Math Use the information about the Bermuda Triangle on page 194 to explain how matrices can be used to find the area covered in this triangle. Then use your method to find the area.

ACT/SAT Find the area of triangle ABC. A 10 units 2 B 12 un its 2 C 14 u nits 2 D 16 u nits 2

REVIEW Use the table to determine the expression that best represents the number of faces of any prism having a base with n sides. F 2(n - 1) H n + 2 G 2( n + 1) J 2n

Write the coordinates of ABC in a vertex matrix. 45. Find the coordinates of A B C . Then graph ABC

Find the coordinates of A B C . Then graph ABC and A B C .

2 -2 4 3  3 -1 9 2 

5 7  1 -4 6 2 

7 6 -5 1 4 3  -1 -2 1 3 -8 2 

MARATHONS The length of a marathon was determined in the 1908 Olympic Games in London, England. The race began at Windsor Castle and ended in front of the royal box at Londons Olympic Stadium, which was a distance of 26 miles 385 yards. Determine how many feet the marathon covers using the formula f(m, y) = 5280m + 3y, where m is the number of miles and y is the number of yards.

slope 1, passes through (5, 3)

slope -_4 3 , passes through (6, -8)

passes through (3, 7) and (-2, -3)

passes through (0, 5) and (10, 10)

x + y = -3 3x + 4y = -12

x + y = 10 2x + y = 11

2x + y = 5 4x + y = 9