Law of Sines (Sec 8-3) — Unit test Answers

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On a coordinate plane, quadrilateral J K L M with diagonals is shown. Point J is at (4, 5), point K is at (5, 1), point L is at (1, 2), and point M is at (1, 5).

Question illustration
A
∠M is a right angle and MK bisects ∠LMJ.
B
LM = JM = 3 and JK = LK = .
Option B
C
MK intersects LJ at its midpoint.
D
The slope of MK is –1 and the slope of LJ is 1.
5

In the diagram, WZ=.

Question illustration
A
units
Option A
B
units
Option B
C
units
Option C
D
units
Option D
6

The vertices of a quadrilateral in the coordinate plane are known. How can the perimeter of the figure be found?

A
Use the distance formula to find the length of each side, and then add the lengths.
B
Use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel.
C
Use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicular.
D
Use the distance formula to find the length of the sides, and then multiply two of the side lengths.
7

In the diagram, DG ∥ EF.

Question illustration
A
DE ≅ GF
B
DE ≅ DG
C
EF ≅ DG
D
EF ≅ GF
8

On a coordinate plane, square P Q R S is shown. Point P is at (4, 2), point Q is at (8, 5), point R is at (5, 9), and point S is at (1, 6).

Question illustration
A
The length of SP, PQ, RQ, and SR are each 5.
B
The slope of SP and RQ is and the slope of SR and PQ is .
Option B
C
The length of SQ and RP are both .
Option C
D
The midpoint of both diagonals is , the slope of RP is 7, and the slope of SQ is .
Option D
10

LMNP is a parallelogram.

Question illustration
A
The length of LM is and the length of MN is .
Option A
B
The slope of LP and MN is –2.
C
LM ∥ PN
D
LP ⊥ PN
11

On a coordinate plane, parallelogram K L M N shown. Point K is at (7, 7), point L is at (5, 3), point M is at (1, 1), and point N is at (3, 5).

Question illustration
A
The midpoint of both diagonals is (4, 4).
B
The length of KM is and the length of NL is .
Option B
C
The slopes of LM and KN are both and NK = ML = .
Option C
D
The slope of KM is 1 and the slope of NL is –1.
12

The vertices of a quadrilateral in the coordinate plane are known. How can the perimeter of the figure be found?

A
Use the distance formula to find the length of each side, and then add the lengths.
B
Use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel.
C
Use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicular.
D
Use the distance formula to find the length of the sides, and then multiply two of the side lengths.
13

On a coordinate plane, rhombus A B C D is shown. Point A is at (1, 1), point B is at (negative 2, negative 3), point C is at (negative 5, 1), and point D is at (negative 2, 5).

Question illustration
A
10 units
B
20 units
C
units
Option C
D
units
Option D
14

On a coordinate plane, rectangle W X Y Z is shown. Point W is at (negative 6, 6), point X is at (negative 4, 0), point Y is at (negative 7, negative 1), and point Z is at (negative 9, 5).

Question illustration
A
units
Option A
B
units
Option B
C
units
Option C
D
units
Option D
15

On a coordinate plane, quadrilateral J K L M with diagonals is shown. Point J is at (4, 5), point K is at (5, 1), point L is at (1, 2), and point M is at (1, 5).

Question illustration
A
∠M is a right angle and MK bisects ∠LMJ.
B
LM = JM = 3 and JK = LK = .
Option B
C
MK intersects LJ at its midpoint.
D
The slope of MK is –1 and the slope of LJ is 1.
16

In the diagram, DG ∥ EF.

Question illustration
A
DE ≅ GF
B
DE ≅ DG
C
EF ≅ DG
D
EF ≅ GF
17

On a coordinate plane, trapezoid J K L M is shown. Point J is at (negative 7, 4), point K is at (negative 4, 4), point L is at (negative 2, 3), and point M is at (negative 8, 3).

Question illustration
A
+ units
Option A
B
2 + + units
Option B
C
9 + units
Option C
D
9 + + units
Option D
18

On a coordinate plane, parallelogram H I J K is shown. Point H is at (negative 2, 2), point I is at (4, 3), point J is at (4, negative 2), and point K is at (negative 2, negative 3).

Question illustration
A
(1,−1)
B
(1,1)
C
(1,0)
D
(0,1)
19

LMNP is a parallelogram.

Question illustration
A
The length of LM is and the length of MN is .
Option A
B
The slope of LP and MN is –2.
C
LM ∥ PN
D
LP ⊥ PN
20

In the diagram, WZ=.

Question illustration
A
units
Option A
B
units
Option B
C
units
Option C
D
units
Option D

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