AnswersA. CostelloWCA 5324 Geometry 1st Nine Weeks 26-27Euclidean Geometry

Directed Line Segments and Modeling Answers

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On a coordinate plane, a line is drawn from point K to point J. Point K is at (160, 120) and point J is at (negative 40, 80).

Question illustration
(
(40, 96)
(
(85, 105)
(
(80, 104)
(
(96, 72)
2
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On a number line, the directed line segment from Q to S has endpoints Q at –8 and S at 12. Point R partitions the directed line segment from Q to S in a 4:1 ratio.Which expression correctly uses the formula to find the location of point R?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

On a coordinate plane, a line is drawn from point A to point B. Point A is at (negative 8, negative 13) and point B is at (4, 11).

Question illustration
(
(1, 5)
(
(0, 3)
(
(–4, –5)
(
(–5, –7)
4

On a coordinate plane, a line is drawn from point A to point B. Point A is at (2, negative 3) and point B is at (negative 4, 9).

Question illustration
A
(0, 1)
B
(–1, 3)
C
(–2, 5)
D
(1, 0)
5

On a coordinate plane, a line is drawn from point J to point K. Point J is at (1, negative 10) and point K is at point (7, 2).

Question illustration
A
–8
B
–5
C
0
D
6
6

If point P is of the distance from M to N, what ratio does the point P partition the directed line segment from M to N into?

Question illustration
A
9:2
B
9:9
C
9:11
D
9:13
7

On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 6, negative 2) and point K is at point (8, negative 9).

Question illustration
A
–4
B
–2
C
2
D
4
8

Why is partitioning a directed line segment into a ratio of 1:3 not the same as finding the length of the directed line segment?

Question illustration
A
The ratio given is part to whole, but fractions compare part to part.
B
The ratio given is part to part. The total number of parts in the whole is 3 – 1 = 2.
C
The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.
D
The ratio given is part to whole, but the associated fraction is .
Option D
9

On a coordinate plane, a line is drawn from point A to point B. Point A is at (7, negative 2) and point B is at (negative 8, negative 9).

Question illustration
A
(–2.2, –6.3)
B
(–2.4, –6.4)
C
(2.7, –0.7)
D
(1.2, –4.7)
10

What is the location of point G, which partitions the directed line segment from F to D into an 8:5 ratio?

Question illustration
A
1
B
2
C
3
D
4
11

On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 6, negative 2) and point K is at point (8, negative 9).

Question illustration
A
–4
B
–2
C
2
D
4
12

Point P partitions the directed line segment from A to B into the ratio 3:4. Will P be closer to A or B? Why?

Question illustration
A
P will be closer to A because it will be the distance from A to B.
Option A
B
P will be closer to A because it will be the distance from A to B.
Option B
C
P will be closer to B because it will be the distance from B to A.
Option C
D
P will be closer to B because it will be the distance from B to A.
Option D
13

On a number line, the directed line segment from Q to S has endpoints Q at –8 and S at 12. Point R partitions the directed line segment from Q to S in a 4:1 ratio.Which expression correctly uses the formula to find the location of point R?

Question illustration
A
(StartFraction 1 Over 1 + 4 EndFraction) (12 minus (negative 8)) + (negative 8)
Option A
B
(StartFraction 4 Over 4 + 1 EndFraction) (12 minus (negative 8)) + (negative 8)
Option B
C
(StartFraction 4 Over 4 + 1 EndFraction) (negative 8 minus 12) + 12
Option C
D
(StartFraction 4 Over 1 + 4 EndFraction) (negative 8 minus 12) + 12
Option D
14

On a coordinate plane, a line is drawn from point J to point K. Point J is at (1, negative 10) and point K is at point (7, 2).

Question illustration
A
–8
B
–5
C
0
D
6
15

If point P is of the distance from M to N, what ratio does the point P partition the directed line segment from M to N into?

Question illustration
A
9:2
B
9:9
C
9:11
D
9:13
16

What is the location of point G, which partitions the directed line segment from F to D into an 8:5 ratio?

Question illustration
A
1
B
2
C
3
D
4
17

The midpoint of a line segment partitions the line segment into a ratio of

A
1:1.
B
1:2.
C
2:1.
D
2:3.
18

On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 15, negative 5) and point K is at (25, 15).

Question illustration
A
(–13, –3)
B
(–7, –1)
C
(–5, 0)
D
(17, 11)
19

Why is partitioning a directed line segment into a ratio of 1:3 not the same as finding the length of the directed line segment?

Question illustration
A
The ratio given is part to whole, but fractions compare part to part.
B
The ratio given is part to part. The total number of parts in the whole is 3 – 1 = 2.
C
The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.
D
The ratio given is part to whole, but the associated fraction is .
Option D
20

On a coordinate plane, a line is drawn from point K to point J. Point K is at (160, 120) and point J is at (negative 40, 80).

Question illustration
A
(40, 96)
B
(85, 105)
C
(80, 104)
D
(96, 72)

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