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
MariettaO [177]
3 years ago
15

show that the points (1 ,7) ,(4, 2), (-1, -1) and (-4, 4) taken in order are the vertics of a square. Also find its area

Mathematics
1 answer:
OLga [1]3 years ago
7 0

Answer:

Step-by-step explanation:

A (1 ,7) ,   B(4, 2),  C(-1, -1) and D(-4, 4)

Find the distance of sides using distance formula.

Distance = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}

A (1 ,7) ,   B(4, 2)

AB = \sqrt{(4-1)^{2}+(2-7)^{2}}\\\\    =\sqrt{3^{2}+(-5)^{2}}\\\\  \\   = \sqrt{9+25}=\sqrt{34} units\\\\\\\\BC = \sqrt{(-1-4)^{2}+(-1-2)^{2}}\\\\ =\sqrt{(-5)^{2}+(-3)^{2}}     = \sqrt{25+9}=\sqrt{34} units\\\\\\CD = \sqrt{(-4-[-1])^{2}+(4-[-1])^{2}}\\\\=\sqrt{(-4+1)^{2}+(4+1)^{2}}\\\\=\sqrt{(-3)^{2}+(5)^{2}}\\\\=\sqrt{9+25} =  \sqrt{34} units\\\\\\AD = \sqrt{(-4-1)^{2}+(4-7)^{2}}\\\\=\sqrt{(-5)^{2}+(-3)^{2}}  =\sqrt{25+9} =  \sqrt{34} units

AB = BC = CD = AD = √34 units. so , ABCD is  a square.

Area of square = side * side

                          = √34 * √34

                          = 34 square units

You might be interested in
A regulation softball has a circumference of 12 inches. what is the volume of the softball?
frez [133]
V=(4/3)pir^2

c=2pir
12=2pir
divide 2
6=pir
divide by pi
6/pi=r

sub for r
V=(4/3)pi(6/pi)^2
V=(4/3)pi(36/(pi^2))
V=(4/3)(36/pi)
V=144/(3pi)
V=48/pi
aprox pi=3.141592
V=15.2788777155

V=15.28 in^3
8 0
3 years ago
If f(1)=4 and f(n)= -2(n-1) -4 then find the value of f(5)
hoa [83]

Answer: f(5) = 43

Step-by-step explanation:

7 0
2 years ago
In a telephone poll, 4 people said that they liked shopping and 10 people said that they don’t like shopping. What is the ratio
Effectus [21]

Answer:

4:10 in simplest form 2:5

Step-by-step explanation:

hope this helps

6 0
3 years ago
Read 2 more answers
How do I find this answer? <br> Not just looking for answer also need explanation
MatroZZZ [7]
55: All triangles measures are equal to 180 degrees. By taking 180 - 75 - 50 you get the angle measure for angle C, which is 55. You know the triangles are congruent, so
8 0
3 years ago
Whats the answer to this?
qaws [65]

Answer: 1,3,5

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • 2:
    10·1 answer
  • Simplify (0.4) to the third power
    8·2 answers
  • What is -2x times x i would try to do it myself but i can't
    15·1 answer
  • A group of friends are sharing 2 &amp; 1/2 lbs of berries. If 5 friends are sharing the berries how many lbs does each friend ge
    14·1 answer
  • in winter, the price of apples suddenly went up by $0.75 per pound. Sam bought 3 pounds of apples at the new price for a total o
    13·2 answers
  • Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per mon
    11·2 answers
  • Tiffany is planning a vacation. The hotel costs $60 per night and her flight costs $220. Tiffany has $600 dollars to spend on th
    9·1 answer
  • What is volume and how is it measured?<br>​
    6·1 answer
  • Which point is best represented by the ordered pair (2, -5.5)?
    15·2 answers
  • you are allowed to work a total of no more that 30 hours each week at your two jobs. lawn mowing pays $5 per hour and babysittin
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!