ame: ________________________ Class: ___________________ Date: __________

ID: A

Competency 4 Geometry Posttest Multiple Choice Identify the choice that best completes the statement or answers the question. Write the equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation.

c.

1. x 2 + 3y 2 − 4x − 5 = 0 a. The equation in standard form is 2 (x − 2 ) + y 2 = 9. The graph of the equation is a circle.

d.

b.

The equation in standard form is 2 (x − 2 ) = 3y 2 . The graph of the equation is a parabola.

1

The equation in standard form is 2 y2 (x − 2) + = 1. The graph of the equation 9 3 is an ellipse.

. The equation in standard form is 2 y2 (x − 2) − = 1. The graph of the equation 9 3 is a hyperbola.


ame: ________________________

ID: A

2. Find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse ÊÁ y + 10 ˆ˜ 2 2 (x − 7) Ë ¯ + = 1. Then of the equation 225 169 graph the ellipse. a. The coordinates of the center are (0, 0), and the coordinates of the foci are (± 2 14 , 0). The lengths of the major and minor axes are 30 units and 26 units respectively. The graph of the ellipse is as follows:

b.

The coordinates of the center are (7, 10), and the coordinates of the foci are (7 ± 2 14 , –10). The lengths of the major and minor axes are 15 units and 13 units respectively. The graph of the ellipse is as follows:

2

c.

The coordinates of the center are (7, –10), and the coordinates of the foci are (7 ± 2 14 , –10 ). The lengths of the major and minor axes are 30 units and 26 units respectively. The graph of the ellipse is as follows:

d.

The coordinates of the center are (–7, 10), and the coordinates of the foci are (7 ± 2 14 , –10 ). The lengths of the major and minor axes are 30 units and 26 units respectively. The graph of the ellipse is as follows:


ame: ________________________

ID: A

Find the distance between the pair of points with the given coordinates.

a.

3. ÊÁË −9, 10ˆ˜¯ and ÊÁË 10, − 3 ˆ˜¯ a. 170 b. c. d.

4 2 530 13

Write the equation for a circle that satisfies the given conditions. 4. center ÊÁË 3, − 7ˆ˜¯ , radius 5 units 2 2 a. (x + 3 ) + ÊÁË y + 7 ˜¯ˆ = 25 2 2 b. (x − 3 ) + ÁËÊ y + 7 ˜¯ˆ = 5 2 2 c. (x − 3 ) + ÊÁË y − 7 ˜¯ˆ = 25 2 2 d. (x − 3 ) + ÊÁË y + 7 ˜¯ˆ = 25 Without writing the equation in standard form, state whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. 5. x 2 + y 2 + 12x − 28y + 111 = 0 a. hyperbola b. parabola c. ellipse d. circle 6. Identify the coordinates of the vertex and focus, the equations of the axis of symmetry and directrix, and the direction of the opening of the parabola with the equation x = 11y 2 − 44y + 33 . Then find the length of the latus rectum and graph the parabola.

3

The coordinates of the vertex and focus are 483 (–11, 2) and (2, − ) respectively. 44 The equations of the axis of symmetry and 485 directrix are y = 2 and x = − respectively. 44 The direction of the opening is right and the 1 unit. length of the latus rectum is 11 The graph of the parabola is as follows:


ame: ________________________

ID: A

b.

The coordinates of the vertex and focus are 483 , 2) respectively. (–11, 2) and (− 44 The equations of the axis of symmetry and 485 directrix are y = 2 and x = − respectively. 44 The direction of the opening is right and the 1 unit. length of the latus rectum is 11 The graph of the parabola is as follows:

d.

The coordinates of the vertex and focus are 1453 (–11, 2) and ( , 2) respectively. 44 The equations of the axis of symmetry and 485 directrix are y = 2 and x = − respectively. 44 The direction of the opening is left and the 1 unit. length of the latus rectum is 11 The graph of the parabola is as follows:

c.

The coordinates of the vertex and focus are 483 , 2) respectively. (–11, 2) and (− 44 The equations of the axis of symmetry and 87 directrix are x = –11 and x = respectively. 44 The direction of the opening is right and the 1 length of the latus rectum is unit. 11 The graph of the parabola is as follows:

Find the center and radius of a circle with the given equation and then graph the circle. 2 2 7. (x − 4 ) + ÊÁË y + 3 ˆ˜¯ = 9 a. The center of the circle is ÊÁË 4, 3 ˆ˜¯ and the radius is 3. The graph of the circle is as follows:

4


ame: ________________________ b.

The center of the circle is ÊÁË −4, 3 ˜ˆ¯ and the radius is 3. The graph of the circle is as follows:

c.

The center of the circle is ÊÁË 4, − 3 ˆ˜¯ and the radius is 9. The graph of the circle is as follows:

ID: A d.

The center of the circle is ÊÁË 4, − 3˜ˆ¯ and the radius is 3. The graph of the circle is as follows:

Write the equation of the ellipse that satisfies the given set of conditions. 8. major axis 16 units long and parallel to the x-axis, minor axis 14 units long, and center at ÁÊË 4, 6 ˜ˆ¯ a. b. c. d.

5

2 (y − 6) 2 (x − 4 ) + =1 256 196 2 x2 y + =1 64 49 2 (y − 6) 2 (x − 4 ) + =1 64 49 2 (y − 6) 2 (x − 4 ) + =1 8 7


ame: ________________________

ID: A

Write an equation for the hyperbola that satisfies the given set of conditions. 9. vertices ÊÁË 14, 0 ˆ˜¯ and ÊÁË −14, 0ˆ˜¯ , conjugate axis of length 4 units y2 x2 − =1 a. 4 196 b. c. d.

y2 x2 − =1 196 4 y2 x2 − =1 196 16 y2 x2 + =1 196 4

10. The vertices of a triangle are P(–3, 8), Q(–6, –4), and R(1, 1). Name the vertices of the image reflected in the x-axis. c. P ′(−3, − 8), Q ′(−6, 4), R ′(1, − 1) a. P ′(3, 8), Q ′(6, − 4), R ′(−1, 1) b. P ′(−3, 8), Q ′(−6, − 4), R ′(1, 1) d. P ′(3, − 8), Q ′(6, 4), R ′(−1, − 1) 11. The vertices of a triangle are P(–7, –4), Q(–7, –8), and R(3, –3). Name the vertices of the image reflected in the line y = x. a. P ′(4, 7), Q ′(8, 7), R ′( 3,− 3) c. P ′(−4, − 7), Q ′(−8, − 7), R ′(−3, 3) b. P ′(4, − 7), Q ′(8, − 7), R ′(3, 3) d. P ′(−4, 7), Q ′(−8, 7), R ′(−3, − 3) 12. Describe in words the translation represented by

14. Find the degree of rotation about the spinner center that maps label i to label g.

the vector 2, − 1 . a. 2 units to the right and 1 units down b. 1 units to the right and 2 units down c. 2 units to the left and 1 units down d. 2 units to the left and 1 units up 13. Write a rule to describe the transformation that is a reflection in the y-axis. a. (x, y) → (x, –y) b. (x, y) → (–x, y) c. (x, y) → (–x, –y) d. (x, y) → (y, x)

a. b. c. d.

6

72° 108° 36° 288°


ame: ________________________

ID: A

15. Identify ∆DEF → ∆HIG as a reflection, translation, rotation, or glide reflection. Find the reflection line, translation vector, center and angle of rotation, or glide vector and reflection line.

a. rotation ; 180° about (–0.5, 0) b. glide vector; and y = 4 c. reflection; x = 5 d. rotation; 180° about (1, 4) 16. How many lines of symmetry does the figure have?

a.

3

b.

2

c.

1

7

d.

0

ID: A

Competency 4 Geometry Posttest Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

C C C D D B D C B C C A B A B A

1