GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment 1. Carmen used a grid to draw a map of the area

around her school. The school is located at (1, 4) on the grid. The softball field is located

at ( 1, 7)− . What is the shortest distance between the school and the softball field?

A. 1 B. 13 C. 5.5 D. 11 Use the graph below to answer question 2. 2. What is the distance between the points on the

graph above? A. 6 B. 18 C. 20 D. 34

Use the grid below to answer question 3. 3. What is the shortest distance between the 2

points on the grid above? A. 5 units B. 7 units C. 5 units D. 7 units 4. In a coordinate plane, what is the distance

between points (5, 6) and (8, 7)? A. 2.8 units B. 3.16 units C. 4.25 units D. 10.0 units

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment 5. Which point is the farthest from the origin (0, 0) on the coordinate plane? A. ( )3, 4− B. ( )5, 1 C. ( )3, 3− D. ( )4, 2− − 6. In a coordinate plane, what is the distance

between points 1( 2,1)P − and 2 (3,4)P ? A. 2.8 units B. 3.2 units C. 4.0 units D. 5.8 units

Use the coordinate plane below to help answer question 7. 7. Triangle ABC isosceles with its vertex angle A

at ( )2, 6− . The coordinates of base angle B are ( )2, 1− . Which could be the coordinates of base angle

C? A. (3, 6) B. (2, 2) C. (3, 1) D. (3, 3)

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment 8. The coordinates of C are ( )1, 1− . The

coordinates of D are ( )9, 9− . What is the

length of CD? A. 128 B. 164 C. 200 D. 328 9. What is the distance between points

E( 2, 3)− and F(4, 1)− , rounded to the nearest tenth of a unit?

A. 3.2 B. 3.5 C. 7.0 D. 7.2

10. Point A has coordinates ( )12, 5− − , and a point

B has coordinates (0, 0). What is the distance between point B and the midpoint of AB?

A. 5 units B. 6.5 units C. 12 units D. 13 units 11. What are the coordinates of point D if ABCD

forms a square? A. ( )0, 10 B. ( )4, 1− C. ( )5, 0 D. ( )6, 1

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment 12. Which of the following points has a distance of

17 units from the origin on a coordinate graph? A. ( )8, 15− − B. ( )4, 21− C. ( )5, 12 D. ( )7, 16 Use the figure below to answer question 13. 13. ABCD drawn above is an isosceles trapezoid.

What is the length of CD? (Round to the nearest hundredth.)

A. 7.00 units B. 9.54 units C. 10.44 units D. 13.45 units

14. What is the approximate distance between

points R and S? A. 5 B. 6.4 C. 9.2 D. 12

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment Use the graph below to answer question 15.

15. What is the distance between A and B above?

(Round your answer to the nearest tenth.) A. 3.6 B. 4.1 C. 6.7 D. 8.1

Use the graph below to answer question 16.

16. Nu needs to walk to the library before she goes

home from school. Which algebraic expression represents the distance she will walk from school directly to the library and then home?

A. 5 + (x + y) B. 5 + x2 + y2 C. 2 25 x y+ + D. 2 25 x y+ + 17. What is the distance between the two points

located at (3, 6) and (7, 9) on a coordinate plane?

A. 5 B. 5 3 C. 7 D. 25

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment Use the map below to answer question 18.

18. Tonya has marked her favorite fishing spots on the map of the lake shown above. What is the distance between the 2 fishing locations?

A. 3 miles B. 26 miles C. 39 miles D. 89 miles 19. R is the midpoint of MN. M is located at

( )4, 3− , and R is located at (6, 1). What is the location of N?

A. (3, 5) B. (5, 2) C. (5, 8) D. (8, 5)

20. Points A and B are the endpoints of a circle’s

diameter. Point A is at ( )8, 5− . Point B is at

( )2, 5− . What are the coordinates of the center of the circle?

A. (0, 3) B. ( )5, 5− C. (3, 0) D. ( )10, 10− 21. Point C is located at ( )3, 6− , and point D is

located at (9,0). What is the midpoint of CD? A. (6, 6) B. ( )6, 3− C. (0, 0) D. (3, 3)

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment Use the figure below to answer question 22. 22. A company uses a computer to cut kites from a

large roll of material. The computer is guided by the coordinates of the four vertices and the intersection of the diagonals of each kite. What are the coordinates of point I, the intersection of the diagonals, in the diagram shown above?

A. ( )5, 2− B. ( )5, 5− C. ( )10, 4− D. ( )10, 10− 23. Triangle ABC has vertices A(2, 2), B(0, 8), and

C (4, 0). What is the midpoint of BC? A. (1, 5) B. (2, 4) C. (3, 1) D. (3, 5)

24. The coordinates of A are (4, 7). The

coordinates of B are ( )10, 2− . What is the

midpoint of AB? A. ( )20, 7− B. ( )3, 4.5− C. (14, 5) D. (7, 2.5) Use the graph below to answer question 25.

25. What are the coordinates of the midpoint of the

midsegment ( )EF of trapezoid ADCB?

A. (1, 2) B. (7, 2) C. (4, 0) D. (4, 2)

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment 26. What are the coordinates of the center of

rectangle ABCD? A. ( )2, 2− B. ( )1.5, 2.5− C. ( )7, 7− D. (7, 7) 27. What is the midpoint of the line segment with

endpoints ( )3, 5− − and ( )7, 5− ? A. ( )5, 5− B. (2, 0) C. ( )2, 5− D. (5, 0)

28. The position of a battleship and a cruiser are

shown in the coordinate system below. The battleship and cruiser are moving toward

each other at the same speed. Which of the following coordinates represent the position where they will meet?

A. ( )1, 3− B. ( )3, 1−

C. 10.5, 22

⎛ ⎞−⎜ ⎟⎝ ⎠

D. 12 , 0.52

⎛ ⎞−⎜ ⎟⎝ ⎠

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment Use the graph below to answer question 29.

29. The diagonals of the figure shown above bisect

each other at point E. Which option correctly represents the coordinates of point E?

A. (5, 3) B. (5.5, 3) C. (5.5, 4) D. (6, 3.5)

30. The segment EF is the diameter of the circle

shown below. Find the coordinates for the center of the circle, which is point G.

A. (3, 5) B. (6, 6) C. (7, 4) D. (14, 8)

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment Use the graph below to answer question 31.

31. What is the midpoint of AC?

A. 1 , 42

⎛ ⎞− −⎜ ⎟⎝ ⎠

B. ( )1, 3−

C. 1 3, 2 2

⎛ ⎞−⎜ ⎟⎝ ⎠

D. 34, 2

⎛ ⎞⎜ ⎟⎝ ⎠

Use the graph below to answer question 32.

32. Point A is located at ( )3, 1− and point B at

( )5, 2− . The midpoint of AB is located at A. (4, 1.5) B. ( )0.5, 1− − C. ( )1, 0.5− D. ( )2, 1− 33. The point (1, 2) is the midpoint of a line

segment whose one endpoint is (–3, 6). What is the other endpoint of the line segment?

A. (–7, 10) B. (–1, 4) C. (4, –4) D. (5, –2)

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment Use the figure below to answer question 34.

34. The figure above shows the location of two

flags on the city’s courthouse grounds. The state flag will be located at the midpoint between the U.S. flag and the city flag. At which point will the state flag be located?

A. 11 5,2 2

⎛ ⎞−⎜ ⎟⎝ ⎠

B. (–3, 5) C. (–1, 2)

D. 3 1,2 2

⎛ ⎞−⎜ ⎟⎝ ⎠

Use the graph below to answer question 35.

35. Tim made a graph of the location of some

playground equipment as shown above. What is the distance between the swings and the slide to the nearest tenth of a unit?

A. 7.1 B. 7.6 C. 12.7 D. 13.0

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment Use the graph below to answer question 36.

36. What is the midpoint of ABshown on the

graph above?

A. (– 92

, 3)

B. ( 32

, 1)

C. (3, 2)

D. ( 92

, –3)

Use the graph below to answer question 37.

(1 unit represents 1 mile.)

37. Points A and B on the graph above represent

the location of two radio towers. Which is the nearest approximation of the distance between the two towers?

A. 8 miles B. 10 miles C. 12 miles D. 16 miles

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment Use the graph below to answer question 38.

38. A designer plotted a map of a client’s home. In one room she placed a lighting fixture as shown on the graph above. How long is this fixture to the nearest tenth of a foot?

A. 5.8 feet B. 7.2 feet C. 9.1 feet D. 10.2 feet

Use the graph below to answer question 39.

39. Which is the distance between points M and N

on the circle shown above to the nearest tenth of a unit?

A. 14.4 B. 17.9 C. 24.5 D. 28.8 40. A 225–miles bike relay had 5 sections.

Marlene rode the 75 to 120 mile section. Water stops were located at the halfway point of each section. Where could Marlene have expected to see a water stop on her portion of the race?

A. 82.5 mile mark B. 90.0 mile mark C. 97.5 mile mark D. 112.5 mile mark

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment Use the graph below to answer question 41.

41. The graph above represents the floor of a new

building. A straight electric cable will be placed from A to C. What is the length of the electric cable to the nearest tenth unit?

A. 5.8 units B. 8.1 units C. 13.5 units D. 19.1 units

Use the graph below to answer question 42.

42. A television weather station is tracking a storm

moving from point A to point B as shown on the graph above. The storm will be at the midpoint of AB in 10 minutes. What are the coordinates of the midpoint of AB?

A. (20, 25) B. (25, 40) C. (30, 35) D. (40, 25)

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment Use the figure below to answer question 43.

43. Which expression will calculate the length of

AB? A. B. C. D. 44. What is the midpoint of a segment with

endpoints of (–3, 5) and (8, –17)? A. (3, –6) B. (5, –12) C. (2.5, –6) D. (–5.5, –9.5)

Use the graph below to answer question 45.

45. The triangle shown above represents a bike

ramp Nate is building. He adds a straight support from point C to the midpoint of AB . What are the coordinates of the midpoint of AB?

A. (7, 2.5) B. (8, 4) C. (9, 3) D. (9, 5.5) 46. The coordinates of point A are (–2, 3). The

coordinates of the midpoint of AB are (6, 1). What are the coordinates of point B?

A. (2, 2) B. (4, –1) C. (–4, 2) D. (14, –1)

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment 47. Which are the coordinates of the midpoint of

AB shown below?

A. (–2, 2) B. (–1, 1) C. (1, –1) D. (0, 2)

48. What is the length of the longest side of

ABCΔ ?

A. 45 B. 109 C. 178 D. 256

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment 49. The city of Jefferson’s system of street blocks

is shown below.

Rounded to the nearest tenth, what is the

distance from the water tower to the grocery store?

A. 10.2 B. 15.3 C. 21.0 D. 25.0

50. What is the length of RS on the graph below?

A. 5 B. 5 C. 7 D. 25

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment 51. What is the midpoint of AB below?

A. (1, 1.5) B. (3, 1.5) C. (2, 2) D. (2, 3)

52. What are the coordinates for the midpoint of

TU below?

A. (–3, 1) B. (–2, 6) C. (–1, 3) D. (3, –1)

GEOMETRY CGT.5.G.1a Use coordinate geometry to find the distance between two points and the midpoint of a segment Use the diagram below to answer question 53.

53. A straight sidewalk passes through a park. One tree is planted along the sidewalk 19 feet from the edge of

the park as shown in the diagram above. Another tree is planted 44 feet from the edge of the park. A fountain will be built along the sidewalk at the midpoint between the two trees. How many feet from the edge of the park will the fountain be built?

A. 12.5 B. 22 C. 25 D. 31.5