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
Fed [463]
3 years ago
6

A rectangle is a four sided flat shape where every integer angle is a right angle. Therefore, opposite sides are parallel and co

nsecutive sides are perpendicular. Rae is drawing rectangle PQRS on a coordinate plane. The rectangle has coordinates P (-1,2), Q(2,4), R(x,y) and S(3,-4)

Mathematics
1 answer:
snow_lady [41]3 years ago
7 0

we know that

The rectangle has coordinates P (-1,2), Q(2,4), R(x,y) and S(3,-4)

using a graph tool

see the attached figure

Step 1

<u>Find the slope of the line PS</u>

the slope is equal to

m=(y2-y1)/(x2-x1)

mPS=(-4-2)/(3+1)=-6/4=-3/2

Step 2

<u>Find the equation of the line QR</u>

we know that

PS and QR are parallel lines

so

their slopes are the same

mQR=-3/2

with mQR and the point Q(2,4) find the equation of the line

y-y1=m*(x-x1)

y-4=(-3/2)*(x-2)

y=(-3/2)*x+3+4--------> y=7-(3/2)*x

Step 3

<u>Find the equation of the line SR</u>

we know that

SR and QR are perpendicular lines

so

the product of their slopes is equal to minus one

mSR*mQR=-1

mSR=2/3

with mSR and the point S(3,-4) find the equation of the line SR

y-y1=m*(x-x1)

y+4=(2/3)*(x-3)

y=(2/3)*x-2-4---------> y=-6+(2/3)*x

Step 4

Find the intersection of the lines QR and SR

we know that

the intersection of the lines QR and SR is the point R

y=7-(3/2)*x------> equation 1

y=-6+(2/3)*x------> equation 2

equate equation 1 and equation 2

7-(3/2)*x=-6+(2/3)*x

7+6=(2/3)*x+(3/2)*x

13=(2/3)*x+(3/2)*x

Multiply by 6 both sides

6*13=4*x+9*x

13*x=6*13

x=6

find the value of y

y=-6+(2/3)*x------> y=-6+(2/3)*6---------> y=-6+4

y=-2

therefore

<u>the answer is</u>

The coordinates of point R are (6,-2)

see the attached figure N 2

You might be interested in
The slope of a line is 2. The y-intercept of the line is –6. Which statements accurately describe how to graph the function?
cupoosta [38]

Answer:A

Step-by-step explanation:

I just did the test and got a 100

5 0
2 years ago
This is the easiest question
Arturiano [62]

Answer:  3\dfrac{2}{6}\ h

Step-by-step explanation:

Given

Rami practices his saxophone for \frac{5}{6} hour on 4 day each week

So, for a week she practices around

\Rightarrow \dfrac{5}{6}\times 4\\\\\Rightarrow \dfrac{20}{6}

Converting it into mixed fraction

\Rightarrow \dfrac{20}{6}=\dfrac{18+2}{6}\\\\\Rightarrow 3\dfrac{2}{6}\ h

5 0
2 years ago
The number of kilograms of water in a human body varies directly as the mass of the body. A 72 kg person contains 48 kg of water
Tanzania [10]

Step-by-step explanation:

N=km

72=k×48

72=48k

k=72/48

k=1.5

N=1.5m

N=1.5×144

N=216

3 0
2 years ago
HELP PLEASE !!!! Rosana used linear combination to solve the system of equations shown. She did so by multiplying the second equ
Allisa [31]
She must have multiplied it by 5.

That would've given her:

x - y = 15
2.5x + y = 25

Now we can add them and the y-terms will eliminate each other. Because one is -y, and the other is positive y. -y + y = 0.
6 0
3 years ago
Read 2 more answers
The number of people who own smartphone to the number of people who owns a flip phone of 4:3 if 500 more people own a smartphone
almond37 [142]

2000 smartphones and 1500 flip phones

4-3=1

1x500=500

500x4=2000

500x3=1500

3 0
3 years ago
Other questions:
  • Suppose you throw a dart at a circular target of radius 10 inches. Assuming that you hit the target and that the coordinates of
    8·1 answer
  • What is 8/9 times 4/7
    5·1 answer
  • Sabrina has designed a rectangular painting that measures 65 feet in length and 30 feet in width. Alfred has also designed a rec
    13·1 answer
  • Find the slope of (1, 2), (-1, -2). Reduce all fractional answers to lowest terms
    9·1 answer
  • A recipe calls for 1/4 cup of chicken broth and 2/6 cup of vegetable broth. what is the total amount of broth needed for the rec
    12·1 answer
  • (15 point) Solve for 14 and 16! The answer could be 58, 11, or 15 for either one. If u get something different let me know.
    9·1 answer
  • Help Me !!! ASAP!!!!
    13·1 answer
  • Find the probability that an SRS of 36 babies will have an average birthweight of over 3.9 kg. Write your answer as a decimal. R
    9·1 answer
  • Find the slope of the lines shown in the graph
    12·1 answer
  • Please give me more points so i can get help
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!