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
lesya [120]
2 years ago
13

Three consecutive vertices of a parallelogram are (– 2, 1); (1, 0) and (4, 3). Find the coordinate of the fourth vertex and find

the area of the parallelogram.
Mathematics
1 answer:
antiseptic1488 [7]2 years ago
6 0

Answer:

D(1,4) - the fourth vertex, the area is equal to 12

Step-by-step explanation:

A(2,-1), B(1,0),C(4,3), They are consecutive, we need to find the point D, find the midpoint of AC (O)

xo= (xA+xc)/2    x0= (-2+4)/2=1

y0=(yA+yC)/2    y0= (1+3)/2=2

0(1,2)

O is the midpoint of BD, so let's find the vertex D

X0= (xB+xD)/2     1= (1+xD)/2   xD=1

y0= (yB+yD)/2      2= (0+yD)/2    yD=4

D(1,4)

the vector DA is (-2-1, 1-4)= (-3,-3)

the vector DC is (4-1, 3-4)= (3,-1)

The modul of DC is sqrt ((-3)^2+(-3)^2)= 3*sqrt2(the length of the side Dc)

The modul of DA is sqrt (3^2+(-1)^2)= sqrt10(the length of the side DA)

cosD= (-3*3+(-3)(-1))/3*sqrt2*sqrt10=-6/3*2*sqrt5=-1/sqrt5

sinD= sqrt (1- 1/5)=2/ sqrt5

S=3sqrt2*sqrt10*2/sqrt5= 12

You might be interested in
A cylinder with a diameter of 10 inches and a height of 12 inches. Determine the area of the cross section formed by slicing the
Colt1911 [192]

Answer:

188.571

if you did directly answer may differ

Step-by-step explanation:

you can see it from the picture above

8 0
2 years ago
For christmas you received an itunes gift card worth $50. you are super excited and can't wait to download justin bieber newest
Greeley [361]

50 divided by 1.25 is 400. 40 songs

4 0
2 years ago
Read 2 more answers
Jasper has an annual salary of $71,000, and his company pays him twice a month. What is the gross income per paycheck that Jaspe
Elan Coil [88]
Divide $71,000 by 24 because there are 12 months in a year and he gets paid 2 times a month. I got $2,958.33
5 0
3 years ago
Read 2 more answers
The surface area of a square pyramid is 84 square inches. The side length of the base is 6 inches. What is the value of x?
s2008m [1.1K]
Umm math is not very important to me ill eventually graduate w a 8.0 GPA
8 0
3 years ago
Suppose your top drawer contains different colored socks: 14 are white, 4 are black, 12 are pink, and 8 are blue. All socks in t
Svetllana [295]

Answer:

8/38

Step-by-step explanation:

you calculate how many socks and then take how many the blue ones are

3 0
3 years ago
Other questions:
  • Can somebody explain what I have to do to find the value of x?<br> (In the pic)
    11·2 answers
  • Geometry math question no Guessing and Please show work thank you
    14·2 answers
  • If you're phone loses 10% after an hour, how long does it take to lose 1%
    12·2 answers
  • Which rectangular shape should the class select for their arts and crafts?12
    13·1 answer
  • Cameron and Sam want to buy a Kindle.
    6·1 answer
  • In the isosceles trapezoid shown, GJ = 5, HI = 9, and GI = 8.6. Determine the length<br><br> of HJ.
    11·1 answer
  • Please help 75 points
    8·2 answers
  • Alena wants 50 people at her birthday party. Due to Corona Virus, she can only have 40% of that total. How many people is she al
    5·1 answer
  • 2(3p-6)+ 4p what is the answer for this
    12·1 answer
  • URGENT, According to the graph below , the slope of line B is
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!