Download GEOMETRY - Study Guide, 1.7, 3.7, 3.8, Ch 5 NAME

GEOMETRY - Study Guide, 1.7, 3.7, 3.8, Ch 5
NAME______________________
1. Find the coordinates of the midpoint of the segment whose endpoints are H(3, 2) and K(9, 14).
2. What is the equation in point-slope form for the line parallel to y = 2x + 9 that contains P(–2, –6)?
3. Write the equation for the horizontal line that contains point G(10, 3).
4. Write the equation for the vertical line that contains point E(–8, –7).
5. What is the slope of the line shown?
(–9, 8)
12 y
10
8
6
4
2
–12–10 –8 –6 –4 –2
–2
–4
–6
–8
–10
–12
2 4 6 8 10
x
(5, –4)
6. What is the graph of
A.
?
C.
y
y
6
6
4
4
2
2
–6 –4 –2
–2
2
4
6
x
–6 –4 –2
–2
–4
–4
–6
–6
2
4
6
x
B.
D.
y
y
6
6
4
4
2
2
–6 –4 –2
–2
2
4
6
–6 –4 –2
–2
x
–4
–4
–6
–6
7. What is the graph of y =
A.
C.
6
x
2
4
6
x
2
4
6
x
y
6
6
4
4
2
2
–6 –4 –2
–2
2
4
6
–6 –4 –2
–2
x
–4
–4
–6
–6
D.
y
y
6
6
4
4
2
2
–6 –4 –2
–2
4
3
x + 3?
4
y
B.
2
2
4
6
x
–6 –4 –2
–2
–4
–4
–6
–6
8. Write an equation in point-slope form of the line through point J(7, –9) with slope 2.
A.
C.
B.
D.
9. Find the midpoint of
y
10
5
Q
–10
–5
5
10 x
P
–5
–10
10. Find the distance between points P(1, 1) and Q(3, 8) to the nearest tenth.
11. What is an equation for the line that passes through points (–6, –10) and (4, 10)?
A. (y – 10) = –2(x – 6)
B. (y – 10) = 2(x – 6)
C. (y + 10) = 2(x + 6)
D. (y + 10) = –2(x + 6)
12. What is an equation in point-slope form for the line perpendicular to y = 3x + 14 that contains (–3, 6)?
13. Noam walks home from school by walking 8 blocks north and then 6 blocks east. How much shorter would his
walk be if there were a direct path from the school to his house? Assume that the blocks are square.
14. Which statement can you conclude is true from the given information?
Given:
is the perpendicular bisector of
A
I
K
J
B
A. B is the midpoint of
B. BK = AK
C.
is a right angle.
D. BI = BK
.
15. For a triangle, list the respective names of the points of concurrency of
• perpendicular bisectors of the sides
• bisectors of the angles
• medians
• lines containing the altitudes
16. Name the point of concurrency of the angle bisectors.
17.
bisects
Find FG. The diagram is not to scale.
E
n+6
F
)
2n – 3
)
D
G
18. What is the orthocenter of the triangle with two altitudes given by the lines
and
?
y
5
(1, 3)
–5
5 (5,x –1)
(–1, –1)
–5
A.
B.
C.
D. none of these
19. Find the length of the midsegment. The diagram is not to scale.
27
38
4x + 3
38
27
3x + 26
20. In ACE, G is the centroid and BE = 15. Find BG and GE.
C
B
A
G
D
F
21. B is the midpoint of
E
D is the midpoint of
and AE = 23. Find BD. The diagram is not to scale.
C
B
D
A
22. In
E
centroid D is on median
.
and
Find AM.
23. Which diagram shows a point P an equal distance from points A, B, and C?
A.
C.
B.
D.
24. Name a median for
|
P
T
)
|
S
)
R
U Q
25. Q is equidistant from the sides of
Find the value of x. The diagram is not to scale.
|
|
|
T
Q
|
)°
13
x+
(5
33°
R
S
26. Find the length of
, given that
is a median of the triangle and AC = 46.
D
A
B
C
27. Write an equation in slope-intercept form of the line through point P(–7, –9) with slope –2.
A. y = –2x – 9
C. y + 9 = –2(x + 7)
B. y = –2x – 23
D. y + 7 = –2(x + 9)
28. Find the value of x.
18
2x – 7
29. Points B, D, and F are midpoints of the sides of
EC = 43 and DF = 17. Find AC.
The diagram is not to scale.
A
B
F
C
D
E
30. Find the circumcenter of the triangle.
y
5
(–4, 2)
–5
(–4, –1)
(0, –1)
–5
5 x
GEOMETRY - Study Guide, 1.7, 3.7, 3.8, Ch 5
NAME______________________
Answer Section
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
(6, 8)
y + 6 = 2(x + 2)
y=3
x = –8
6
7
B
D
D
(1, –1)
7.3
C
1
y – 6 =  (x + 3)
3
4 blocks
D
circumcenter
incenter
centroid
orthocenter
C
15
B
19
16.
17.
18.
19.
20.
21. 11.5
22. 9
23. B
24.
25.
26.
27.
28.
29.
4
23
B
8
34
30. (2,
1
)
2