Geometry – Spring Break Homework

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Geometry – Spring Break Homework

1. A function is described by the ordered pairs If the given function is translated 2 units to the right and then reflected across the x-axis, what are the ordered pairs that describe the transformed function?

A.

B.

C.

D.

2. A rectangle is shown on the coordinate plane below. Identify a line that the rectangle could be reflected over to result in a rectangle that has the same vertices as the original.

A.

B.

C.

D.

3. The vertices of triangle ABC have coordinates A, B, and C What are the coordinates of point B after triangle ABC is reflected across the x-axis and then rotated 90 degrees around?

A.

B.

C.

D.

4. Vinnie is trying to prove . Which statement would not help to prove the two triangles congruent?

A.

B.

C.

D.
5. Based on the following figure, determine which values below are correct. Select all that apply.

A.

B.

C.

D.

E.

F.
6. Examine ΔABC below. Which of the following equations correctly represent the relationships between the segments? Select all that apply.

A.

B.

C.

D.

E.

F.

7. Examine parallelogram below. Determine which of the following values are correct. Select three that apply.

A.

B.

C.

D.

E.

F.

8. Anne is writing a proof about the figure shown on the coordinate plane below. She wants to show that quadrilateral ABCD is a parallelogram. Which of these is a correct, complete plan for Anne's proof?

A. Show that and have equal slopes.

B. Show that and have the same length.

C. Show that the midpoints of and are the same point.

D. Show that and have slopes that are negative reciprocals of each other.

9. What type of compass and straightedge construction is being made in the figure to the right?

A. an angle bisector

B. a perpendicular bisector to line

C. a line parallel to line

D. a line through that is parallel to line

10. Trapezoid shown below is dilated about the origin by a scale factor of to produce trapezoid . What is the relationship between and ?

A. The lines are parallel and have the same slope.

B. The lines are parallel and have reciprocal slopes.

C. The lines intersect and have opposite slopes.

D. The lines are perpendicular and have opposite reciprocal slopes.

11. Carolina drew 12 units long on a coordinate plane. Her dilated line segment is parallel to which measures 15 units long. What was the scale factor of dilation for the line segment Carolina drew?

A. B. C. D.

12. A diagram is shown below. Which statements show that is similar to ? Select all that apply.

A.

B.

C.

D. and

E. and

13. Based on the drawing below, in order for to be similar to by SAS similarity, which of the following needs to be true?

A.

B.

C.

D.
14. Examine the following figure in which was dilated and then reflected across the given line to create .

If and which statement must be true?

A. and

B. and

C. and

D. and

15. Carla believes that is similar to . She believes that a set of transformations to can turn it into . Which set of transformations below will prove that the two triangles are similar?

A. a 180° rotation about the origin followed by a dilation of 1.5 centered at the origin

B. a 180° rotation about the origin followed by a dilation of 1.5 centered at point (2, 2)

C. a 90° rotation about the origin followed by a dilation of 1.5 centered at point (–2, 2)

D. a 90° rotation about the origin followed by a dilation of 1.5 centered at the origin
16. Thomas is attempting to prove the Pythagorean Theorem using similar triangles. Which of the following could be Thomas's first ratio that he sets up?

A.

B.

C.

D.

17. In the triangle below, measures 12 cm and measures 13 cm. What is the ratio of side lengths to ?

A. 12:5

B. 13:5

C. 144:25

D. 169:25

18. In the figure below, . Determine the length of .

A. 3

B. 9

C. 12

D. 14

19. Triangle is similar to triangle Select all angles whose sine equals .

A. B

B. F

C. L

D. M

E. R

F. T
20. In order for , what must be the measure of ?

A. 37° B. 53° C. 90° D. 127°

21. Jay and Libby are working outside when they see a blimp flying over the neighborhood. Jay is mowing the lawn approximately 2,500 feet (ft) from Libby when they both see the blimp. Libby looks up from her gardening at an angle of while Jay looks up at an angle of . Which distance, in feet, is closest to the vertical height of the blimp above the ground?

A. 1,751 feet

B. 2,331 feet

C. 7,027 feet

D. 7,535 feet
22. On a sunny day, Elliot notices that a lamp post casts a shadow on the ground. If the shadow is 18 ft long and the lamp post is 13 ft tall, what is the angle of elevation of the sun? (Assume the lamp post is at a right angle to the ground.)

A. 35.84°

B. 43.76°

C. 46.24°

D. 54.16°

23. The figure below shows the circles and. Which of these statements can be used to prove that the circles are similar?

A. The circles and are similar because can be mapped onto by a translation two units to the right and three units up followed by a dilation about its center by a scale factor of .

B. The circles and are similar because can be mapped onto by a translation two units to the right and three units up followed by a dilation about its center by a scale factor of 2.

C. The circles and are similar because can be mapped onto by a translation two units to the left and three units down followed by a dilation about its center by a scale factor of .

D. The circles and are similar because can be mapped onto by a translation two units to the left and three units down followed by a dilation about its center by a scale factor of 2.

24. Prove that Circle A and Circle B are similar. Circle A: center (–3, 2) and radius of 2 units. Circle B: Center (6, –1) and a radius of 3 units. Select the option that best shows the necessary transformations from Circle A to Circle B.

A. move left 9 units; up 3 units; and a reduction of radius by 2

B. move right 9 units; down 3 units; and an increase of radius with a ratio of

C. move right 9 units; down 3 units and an increase of radius with a ratio of

D. move left 9 units; up 3 units; and a reduction of radius by
25. You are standing 16 feet from the center of a circular swimming pool. The distance from you to a point of tangency is 25 feet. What is the approximate DIAMETER of the pool?

A. 12 ft

B. 19 ft

C. 23 ft

D. 38 ft

26. Find if and .

A. 18°

B. 60°

C. 78°

D. 156°

27. Quadrilateral ABCD is inscribed in circle O. If mA = 88°, what is mC?

A. 88°

B. 90°

C. 92°

D. Cannot be determined

28. If is the radian measure of a central angle of a circle and r is the radius of the circle, which is the correct derivation of the area, A, of the sector bounded by the sides of the central angle and the arc it subtends?

A.

B.

C.

D.

29. The Thompson Family made a circular cheesecake with a radius of 4 inches for dessert. The area of the cheesecake can be found by using the formula or . Mrs. Thompson cut out a piece that has a central angle of 39°, as shown below. What is the formula for the area of the piece that Mrs. Thompson cut out?

A.

B.

C.

D.

30. A circle drawn on a coordinate plane has the equation . Select each true statement regarding this circle.

A. The circle has a radius of 4 units.

B. The circle has a radius of units.

C. The center of the circle is located at the point (4, –4).

D. The center of the circle is located at the point (–4, 4).

E. The equation of the circle can be written as .
31. A diameter of a circle has endpoints of (–5 , 6) and (–5 , –2). What is the equation of this circle?

A.

B.

C.

D.

32. Three vertices of quadrilateral are as shown below. In order for to be a parallelogram, what must be the coordinates of point C?

A.

B.

C.

D.

33. Which of the following best describes the classification of quadrilateral ABCD given the coordinates of A, B, C, and D?

A. parallelogram

B. rectangle

C. rhombus

D. square
34. Find the equation of a line through the coordinate (3 , –2) and parallel to the line represented by .

A.

B.

C.

D.
35. What is the y–intercept of a line perpendicular to that passes through the point ?

A.

B.

C.

D.

36. Examine the following coordinate grid. Point is the midpoint of . There exists a point that is located on and is one-third of the way from to . What are the coordinates of ?

A.

B.

C.

D.

37. A triangle is shown on the coordinate plane. What is the perimeter of this triangle rounded to the nearest tenth of a unit?

A. 31.0 units

B. 34.0 units

C. 37.5 units

D. 40.4 units
38. A city planner laid out a small town on a grid, where each unit on the grid is 10 feet by 10 feet or 100 square feet. The town's park is shown on the grid below. Select all of the options that are true about the area and perimeter of the park (round the area to the nearest 100 square feet and the perimeter to the nearest 10 feet).

A. The area of the park is 3200 square feet.

B. The area of the park is 3400 square feet.

C. T14he area of the park is 4400 square feet.

D. The3 ,perimeter of the park is 240 feet.

E. The perimeter of the park is 250 feet.

F. The perimeter of the park is 300 feet.
39. Sarah is measuring parts of circular objects to find the value of . She measures the distance around a circle the radius and the diameter. Which relationship would result in the value of ?

A.

B.

C.

D.
40. Point divides the line segment joining points and such that . What are the coordinates of point ?

A.

B.

C.

D.