1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Talja [164]
2 years ago
9

Which statement BEST describes a parallelogram with coordinates A (-1, 0), B (-4, 5), C (1, 8) and D (4, 3)? A. The diagonals ar

e congruent which means the quadrilateral is a rectangle. B. The diagonals are perpendicular which means the quadrilateral is a rhombus. C. The diagonals are both congruent and perpendicular which means the quadrilateral is a square. D. The diagonals are neither congruent nor perpendicular, which means the quadrilateral is a parallelogram only.
Mathematics
1 answer:
klio [65]2 years ago
4 0
<h2>Answer:</h2>

D.

<h2>Step-by-step explanation:</h2>

The representation of this problem is shown below. To find the answer, we need to use the distance formula:

The \ \mathbf{distance} \ d \ between \ the \ \mathbf{points} \ (x_{1},y_{1}) \ and \ (x_{2},y_{2}) \ in \ the \ plane \ is:\\ \\ d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}

  • The first diagonal is formed by the points A and C
  • The second diagonal is formed by the points B and D

So, for the first diagonal:

A(x_{1},y_{1})=A(-1,10) \\ \\ C(x_{2},y_{2})=C(1,8) \\ \\ \\ d_{1}=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2} \\ \\ d_{1}=\sqrt{[1-(-1)]^2+(8-10)^2}=2\sqrt{2}

For the second diagonal:

B(x_{1},y_{1})=B(-4,5) \\ \\ D(x_{2},y_{2})=D(4,3) \\ \\ \\ d_{2}=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2} \\ \\ d_{2}=\sqrt{[4-(-4)]^2+(3-5)^2}=2\sqrt{17}

So the diagonals aren't congruent. Are they perpendicular?

\vec{AC}=(1,8)-(-1,10)=(2,-2) \\ \\ \vec{BD}=(4,3)-(-4,5)=(8,-2)

These two vectors will be perpendicular (hence the diagonals will be perpendicular) if and only if the dot product equals zero, so:

(2,-2).(8,-2)=2(8)+(-2)(-2)=20\neq 0

Thus, the diagonals aren't perpendicular. In conclusion:

<h3>D. The diagonals are neither congruent nor perpendicular, which means the quadrilateral is a parallelogram only.</h3>
You might be interested in
Consider the function given by the graph. What are
horrorfan [7]

Answer:

the values of it is the first one. meaning: f(-2)

8 0
3 years ago
Find the y-intercept and the slope of the line.<br> 6x-2y=5
solmaris [256]

Answer:

m=3

b=(0,5)

Step-by-step explanation:

6 0
1 year ago
A lift driver charges $5.25 for the first mile of the trip and$1.25 each mile after that. He charges the customer $24 for the ri
WARRIOR [948]

Answer: 15 miles

Step-by-step explanation:

The equation is 5.25+1.25x=24 where x is each additional mile so to solve for x it would be  1.25x=18.75 and divide both sides to solve for x

3 0
3 years ago
Read 2 more answers
In ΔXYZ, y = 53 inches, z = 55 inches and ∠X=120°. Find the length of x, to the nearest inch.
djverab [1.8K]

Answer: 94

Step-by-step explanation:

4 0
2 years ago
Suzanne wants to put a fence around her square garden. If the garden covers an area of 64 ft^2, how many feet of fencing does sh
Art [367]

Answer:

32 feet of fence

Step-by-step explanation:

The garden is a square, so the length and width are equal.

A = L x W

W = L

A = W²

A = 64

W² = 64

W = √64 = ±8 -- (-8) would be extraneous

W = 8 ft

L = 8ft

Since she is putting the fence around the garden, she needs to find the perimeter.

P = 2L + 2W

P = 2(8) + 2(8)

P = 16 + 16

P = 32 ft

32 feet of fence

8 0
3 years ago
Other questions:
  • How many deciliters are equivalent to 9 cups? Use the conversion table to find the answer. Round to the nearest tenth.
    7·2 answers
  • Best answer will get 100 pts + brainliest!
    11·2 answers
  • In the triangle below x=? Round to the nearest tenth. Please help!
    13·1 answer
  • The coordinates of the vertices of a polygon are (−2, −2) , (−2, 3) , (2, 4) , (3, 1) , and (0, −2) .
    8·1 answer
  • Which equations have the same value of x as 5 (30x-15) = <br>72​
    6·1 answer
  • What is the distributive property of the GCF of 36 and 45 to rewrite the sum
    7·1 answer
  • Anyone willing to help me out?
    13·1 answer
  • 8 ÷ 2 × ( 5 + 5 ) this is not what im.paying for
    9·2 answers
  • A number divided by four is at most 6. Which choice is correct??
    9·1 answer
  • A rocket is traveling 4,000 miles per hour. How much time in hours will it take the rocket to travel a distance of 84,000 miles?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!