Mathematics Calculations

Calculate the area of the triangle with the following vertices using matrices.

1. (0,-9), (3,-9), and (0,-2)

A. 21 units²

B. 10.5 units²

C. 16.5 units²

D. 33 units² 

2. (-8, -2), (-1, -11), and (-1, -2)

A. 63 units²

B. 121 units²

C. 31.5 units²

D. 60.5 units²

3. (-5, 1), (2, 9), and (-5, 9)

A. 56 units²

B. 28 units²

C. 120 units²

D. 60 units²

Show how you use matrices to write an equation for a line that passes through the following points:

4. (4, -10), (1, -1)

A. y = –¹¹/₃x + 2 

B. y = 3x – 2 

C. y = ¹¹/₃x – 2 

D. y = -3x + 2

Classify the conic section of each equation.

5. 25x² – 9y² = 144

A. Hyperbola

B. Parabola

C. Ellipse

D. Circle

6. x² + y² = 225

A. Parabola

B. Hyperbola

C. Ellipse

D. Circle

7. x² + 3y² = 3

A. Ellipse

B. Hyperbola

C. Parabola

D. Circle

8. 4x² + 3x = y² + 2y + 7

A. Ellipse

B. Parabola

C. Hyperbola

D. Circle 

Answer each question. 

9. What is the standard equation of the circle whose center is (-5,-4) and whose radius is 3?

A.  (x+5)² + (y+4)² = 9

B. (x – 5)² + (y – 4)² = 9

C. (x+5)² + (y+4)² = 3

D. (x – 5)² + (y – 4)² = 3

10. What are the center and radius of the circle whose equation is x² + (y-3)² = 144?

A. Center is (0,-3); radius is 12

B. Center is (0,3); radius is 144

C. Center is (0,3); radius is 12

D. Center is (3,0); radius is 12

11. What are the four vertices of the ellipse whose equation is (x²)/9 + (y²)/4 = 1?

A. Vertices are (3,0), (-3,0)

B. Vertices are (0,2), (0,-2)

C. Vertices are (2,0), (-2,0), (0,3), (0,-3)

D. Vertices are (3,0), (-3,0), (0,2), (0,-2)

12. What is the center of the hyperbola whose equation is [(x+4)² / 9] – [(y-3)² / 16] = 1?

A. (-4,3)

B. (4,-3)

C. (-3,4)

D. (3,-4)

13. How does the graph of the hyperbola open, if its equation is [(x²) / 25] – [(y²) / 36] = 1?  Explain how you know just by looking at the equation.

A. Opens to sides (x²-term is negative)

B. Opens to sides (y²-term is negative)

C. Opens up-and-down (x²-term is negative)

D. Opens up-and-down (y²-term is negative)

14. How does the graph of the hyperbola open, if its equation is [(y²) / 36] – [(x²) / 25] = 1?  Explain how you know just by looking at the equation.

A. Opens up-and-down (x²-term is negative)

B. Opens up-and-down (y²-term is negative)

C. Opens to sides (y²-term is negative)

D. Opens to sides (x²-term is negative)

15. What is the eccentricity of the ellipse whose equation is [(x²) / 25] +[(y-3)² / 9] = 1?

A. ³/₅

B. ⁵/₄

C. ⁵/₃

D. ⁴/₅

16. Using Cramer’s rule, what is the value of D_x when calculating the determinant?

5x – y = 2
3x – 2y = 1 

A. -7

B. -3

C. -1

D. -5

17. The correct determinant value for the determinant  would be:

A. (7)(5) – (8)(2)

B. (7)(2) – (5)(8)

C. (7)(8) – (5)(2) 

D. (7)(2)(5)(8)

18. In Matrix A, what element is in the second row, third column?

A. 1.5

B. 6

C. 2

D. 1

19. Calculate the determinant:

A. 14

B. 10

C. -14

D. -10

20. State the center of the conic:

hyperbola whose equation is [(x – 1)² / 16] – [(y + 3)² / 9] = 1

A. (3, -1)

B. (1, -3)

C. (4, 3)

D. (-1, 3)