Name: 
 

Ch 1 Gateway



 1. 

The coordinates of the midpoint of mc001-1.jpg are (5, 0), and the coordinates of A are (2, 3). What are the coordinates of B?
A)
(3.5, 1.5)
B)
(–1, 6)
C)
(8, 3)
D)
(8, –3)
 

 2. 

What is mÐ3?
 mc002-1.jpg
A)
67°
B)
68°
C)
78°
D)
90°
 

 3. 

The Department of Transportation
wants to extend the intersecting road across the highway, as indicated by the dotted line.




What should x be to ensure that the intersecting road and the new construction form a straight line?
mc003-1.jpg
A)
41°
B)
49°
C)
111°
D)
131°
 

 4. 

In the diagram,
mÐ1 = (7x – 6)° and
mÐ2 = (6x + 13)°

Which is closest to the value of x?
mc004-1.jpg
A)
7.0
B)
13.3
C)
14.4
D)
19.0
 

 5. 

What is the midpoint of the segment joining (13, 4) and mc005-1.jpg?
A)
(12, 19)
B)
mc005-3.jpg
C)
(9.5, 6)
D)
mc005-4.jpg
 

 6. 

What are the apparent coordinates
of the midpoint of diagonal mc006-1.jpg?
mc006-2.jpg
A)
(0.5, 0)
B)
(0, 0.5)
C)
(0, 0)
D)
(0.5, 0)
 

 7. 

What are the values of x, and y?
 mc007-1.jpg
A)
x = 88°, y = 103°
C)
x = 98°, y = 103°
B)
x = 88°, y = 113°
D)
x = 98°, y = 113°
 

 8. 

The measures of some angles
are given in the figure.



What is the value of x?
mc008-1.jpg
A)
64°
B)
63°
C)
86°
D)
85°
 

 9. 

If the coordinates of A are (3, 3) and the midpoint of mc009-1.jpg is mc009-2.jpg, then the
coordinates of B are --
A)
mc009-3.jpg
B)
(1.5, 1.5)
C)
mc009-4.jpg
D)
mc009-5.jpg
 

 10. 

Angle 1 is a supplement of angle 2. If mÐ1 = (14x – 62)º and mÐ2 = (4x + 26)º, what is the value of x and of mÐ1?
A)
x = 12, mÐ1 = 106°
C)
x = 7, mÐ1 = 36°
B)
x = 12, mÐ1 = 74°
D)
x = 7, mÐ1 = 54°
 

 11. 

In the figure shown,
mÐ 1 = (5x + 10)° and
m
Ð 2 = (3x + 32)°.








What is mÐ 1 ?
mc011-1.jpg
A)
42°
B)
40°
C)
50°
D)
55°
 

 12. 

Triangle ABC is placed on
a grid as shown.










The apparent midpoint of mc012-1.jpg is:
mc012-2.jpg
A)
(4, 4)
B)
(1, 4)
C)
(2.5, 5.5)
D)
(2.5, 2.5)
 

 13. 

A plumber bent a flexible joint into a
135° angle, as shown.  He then attached another pipe so that A, B, and D lay on a straight line.

What is the value of x?
mc013-1.jpg
A)
35
B)
45
C)
43
D)
225
 

 14. 

The measures of some angles
are given in this figure.





What is the measure of ÐN?
mc014-1.jpg
A)
40°
B)
63°
C)
77°
D)
117°
 

 15. 

A gardener rested his hoe against a shed.
The hoe made a 47° angle with the ground as shown in the diagram below.






                                  
Which represets the supplement to the 47° angle?
mc015-1.jpg
A)
w
B)
x
C)
y
D)
z
 

 16. 

Two lines intesect as shown.





What is the value of x?
mc016-1.jpg
A)
9
B)
15
C)
125
D)
10
 

 17. 

What are the measures of two complementary angles if the difference of their measures is 26°?
A)
32°, 58°
B)
39°, 51°
C)
77°, 103°
D)
84°, 96°
 

 18. 

P(–5,7), Q(–1,9), R(6,3), and S(–6,–3)
are connected to form a trapezoid.













What is the midpoint of mc018-1.jpg?
mc018-2.jpg
A)
(–2, –4)
B)
(2, –2)
C)
(1, –2.5)
D)
(0, 0)
 

 19. 

Parallelogram ABCD is positioned
on a coordinate plane with the coordinates as shown. 

N is the midpoint of mc019-1.jpg


What are the coordinates of N?
mc019-2.jpg
A)
(5.5, 3)
B)
(10.5, 9)
C)
(7, 11.5)
D)
(11.5, 7)
 

 20. 

Which pair of angles is complementary?
A)
mc020-1.jpg
C)
mc020-3.jpg
B)
mc020-2.jpg
D)
mc020-4.jpg
 

 21. 

A line segment has an endpoint at (–7, 3).  If the midpoint of the line segment is (–4, –2), what are the coordinates of the point at the other end of the line segment?
A)
(–5.5, 0.5)
B)
(–10, 8)
C)
(–1, 5)
D)
(–1, –7)
 

 22. 

Which point is the greatest distance from the origin?
A)
(–5, 5)
B)
(2, –2)
C)
(–2, –2)
D)
(–3, –3)
 

 23. 

Lines AB and CD intersect at P.
mc023-1.jpg is perpendicular to mc023-2.jpg,
and mÐAPD = 167°.

What is the measure of ÐDPB?
mc023-3.jpg
A)
13°
B)
23°
C)
33°
D)
43°
 

 24. 

Parallelogram ABCD is placed
on a coordinate grid as shown.










What is the approximate length of diagonal mc024-1.jpg?
mc024-2.jpg
A)
6.0 units
B)
2.0 units
C)
2.8 units
D)
3.6 units
 

 25. 

A guy wire for a pole for a
tennis net makes an angle of 61° with the ground.

What is the measure of the angle between the wire and the pole?
mc025-1.jpg
A)
29°
B)
61°
C)
90°
D)
180°
 



 
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