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
Oksi-84 [34.3K]
3 years ago
5

The coordinates of the vertices of quadrilateral ABCD are A(4,1) B(1,5) C(-3,2) and D(0,-2). Prove the quadrilateral is a square

.
Mathematics
1 answer:
Vanyuwa [196]3 years ago
5 0

Answer:

The quadrilateral is a SQUARE.

Step-by-step explanation:

Given

Four points

A(4,1)  

B(1,5)

C(-3,2)

D(0, -2)

The quadrilateral formed will be ABCD with sides AB, BC, CD, AD. In order to prove if a quadrilateral is a square we have to prove that all sides of the quadrilateral are equal.

We will use the two-point distance formula to calculate lengths of sides of quadrilateral.

The distance formula:

d= √((x_2- x_1)^2+(y_2- y_1)^2  )

So, for side AB

AB= √((1- 4)^2+(5- 1)^2  )

= √((-3)^2+(4)^2  )

= √(9+16)

= √25

= 5 units

For BC

BC= √((-3- 1)^2+(2- 5)^2  )

= √((-4)^2+(-3)^2  )

= √(16+9)

= √25

= 5 units

For CD

BC= √((0-(-3))^2+(-2-2)^2  )

= √((0+3)^2+(-4)^2  )

= √(9+16)

= √25

= 5 units

For AD

AD= √((0-4)^2+(-2-1)^2  )

= √((-4)^2+(-3)^2  )

= √(16+9)

= √25

= 5 units

As all the sides are equal

AB=BC=CD=AD

= 5 units

So the quadrilateral is a square.

2 dot.

You might be interested in
Add. Write your answer as a fraction in simplest form.<br> -4/8 + (-23/18)
abruzzese [7]

Answer:

sorry i need more points

Step-by-step explanation:

8 0
3 years ago
PLS HELP ASAP. Thank you! <br><br><br> Will mark brainliest.
AlekseyPX

Answer:

Volume: 2047.5 in. cubes

surface area: 1067.5 in.

3 0
3 years ago
Monica's school band held a car wash to raise money for
Ksivusya [100]

Answer:

1 is 50 and 2 is 75

Step-by-step explanation:

i did the work

3 0
3 years ago
Given h(x) = x2 – 5x + 7, find the following.<br> a. h(2)<br> b.h(-5)<br> c. h(-8)
azamat

Answer:

Step-by-step explanation:

hello :

h(x) = x² – 5x + 7

h(-2) = (-2)² – 5(-2) + 7 =4+10+7 =21

h(-5) = (-5)² – 5(-5) + 7= 25+25+7 =57

h(-8) = (-8)² – 5(-8) + 7 = 64+40+7=111

5 0
3 years ago
James divided the candy bar<br>into 4 parts.<br>He gave 1 part to his friend.​
photoshop1234 [79]

Answer:

If he gave 1 part to his friend then he will have 3 parts left. Is that what you needed help on?

7 0
3 years ago
Other questions:
  • I need help please
    11·2 answers
  • Which of these numbers rolands to 7.6?<br> 7546<br> • 7630<br> 7670<br> 7720
    11·1 answer
  • How do you solve this ?
    9·1 answer
  • Which pair of ratios forms a proportion?​
    9·2 answers
  • Your family of 5 went to the Chinese buffet. The cost for each person was $8.95. The sales tax was
    15·1 answer
  • Select all the expressions that are equivalent to .
    14·1 answer
  • QUICK!! NEED HELP ASAP!!!
    14·1 answer
  • Brad baked 36 muffins. Adam baked 8 more muffins than Brad.
    9·2 answers
  • PLSSS HELP IF YOU TURLY KNOW THISS
    13·1 answer
  • 3
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!