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
Fudgin [204]
3 years ago
12

The coordinates of quadrilateral PQRS are P(–3, 0), Q(0, 4), R(4, 1), and S(1, –3). What best describes the quadrilateral?

Mathematics
1 answer:
denis-greek [22]3 years ago
4 0

Answer:

Square

Step-by-step explanation:

Plot the vertices of the quadrilateral PQRS on the coordinate plane (see attached diagram). The diagram shows that this is a square. Let's prove it.

1. Find all sides lengths:

PQ=\sqrt{(-3-0)^2+(0-4)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\ \\QR=\sqrt{(0-4)^2+(4-1)^2}=\sqrt{(-4)^2+(3)^2}=\sqrt{16+9}=\sqrt{25}=5\\ \\RS=\sqrt{(4-1)^2+(1-(-3))^2}=\sqrt{(3)^2+(4)^2}=\sqrt{9+16}=\sqrt{25}=5\\ \\SP=\sqrt{(1-(-3))^2+(-3-0)^2}=\sqrt{(4)^2+(-3)^2}=\sqrt{16+9}=\sqrt{25}=5

All sides have the same lengths.

2. Find the slopes of all lines:

PQ:\ \dfrac{4-0}{0-(-3)}=\dfrac{4}{3}\\ \\QR:\ \dfrac{1-4}{4-0}=-\dfrac{3}{4}\\ \\RS:\ \dfrac{-3-1}{1-4}=\dfrac{4}{3}\\ \\SP:\ \dfrac{0-(-3)}{-3-1}=-\dfrac{3}{4}

Since the slopes of PQ and RS are the same, lines PQ and RS are parallel. Since the slopes of QR and SP are the same, lines QR and SP are parallel.

The slopes \frac{4}{3} and -\frac{3}{4} have the product of

-\dfrac{3}{4}\cdot \dfrac{4}{3}=-1,

then lines are pairwise perpendicular.

This means PQRS is a square.

You might be interested in
How do I unsubscribe from here
Naddik [55]

Answer:

usub from where

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Jimmy had $4.52 to spend. He found something he wanted to buy for $6.21. How much would he need to borrow from his friend to mak
Inessa05 [86]
He would need to borrow $1.69
6 0
3 years ago
Read 2 more answers
Ninety members of a gym were asked whether or not they use a treadmill when they exercise and whether or not they lift weights w
mamaluj [8]

The answer is Y

Step-by-step explanation:

You have to compare the numbers with conditions both in Rows and Columns.

5 0
1 year ago
Factor the expression.
nalin [4]
6x^2+14x+4
First factor out all numerical factors (=2 in this case)
2(3x^2+7x+2)
look for m,n such that m*n=3*2, m+n=7 => m=6, n=1
2(3x^2+6x  + 1x+2)
Factor 3x^2+6x into 3x(x+2)
2( 3x(x+2)+1(x+2) )
factor out common factor (x+2)
2(x+2)(3x+1)
=>
6x^2+14x+4=2(x+2)(3x+1)
8 0
3 years ago
1) Suppose you put money into two different bank accounts. In account #1 you deposit $500 and you will be earning 6% interest co
Elis [28]
The answer for number 1 is D they will have the same amount of money.

6 0
3 years ago
Read 2 more answers
Other questions:
  • The ages (in years) of eight passengers on a bus are listed below.
    7·2 answers
  • The net below can be folded to form a square pyramid.
    12·2 answers
  • ricardo has a marble collection with 54 blue marbles, 24 red marbles, and 18 yellow marbles. He arranges the marbles into equal
    13·2 answers
  • Jesse takes his dog and cat for their annual vet visit. Jesse's dog weighs 23 pounds. The vet tells him his cats weight is 5/8 a
    7·1 answer
  • In a recent snail race,the winning snail traveled 5.85 cm 3/4 of a minute. How fast was the snail traveling in centimeters per s
    5·2 answers
  • Solve each equation.<br> X – 10 = 4<br> Math
    12·2 answers
  • Make a the subject of the formula:<br> v=u + at
    5·1 answer
  • ACTIVITY 1
    5·1 answer
  • Question 3 2 pts Here is a story: Diego bought 4 boxes of cookies to thank his coaches at the end of the season. Each box had th
    15·2 answers
  • IMPORTANT PLEASE HELP<br><br> Table tennis question
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!