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
Eduardwww [97]
2 years ago
15

Please help! find the distance of AG if A (4,4) and G (-1,-1)

Mathematics
2 answers:
Naya [18.7K]2 years ago
8 0

  • The distance between two points \rm{A(x_1,y_1)} and \rm{B(x_2,y_2)} is given by the formula,

\rm{AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }

Proof:

\rm{Let  \: X'OX \:  and  \: YOY' \:  be \:  the \:  z-axis  \: and \:  y-axis  \: respectively. Then, O \:  is \:  the \:  origin.}

\rm{Let  \: A(x_1,y_1)  \: and  \: B(x_2,y_2)  \: be \:  the \:  given \:  points.}

\rm{Draw \:  AL \perp \: OX, BM \perp \: OX  \: and  \: AN \perp BM }

Now,

\rm{OL=x_1,OM=x_2,AL=y_1  \: and \:  BM=y_2}

\rm\therefore{AN=LM=(OM-OL)=(x_2-x_1)}

\:  \:  \:  \:  \rm{BN=(BM-NM)=(BM-AL)=(y_2-y_1)}

\rm{In  \: right  \: angled \:  \triangle ANB, by  \: Pythagorean  \: theorem,}

We have,

\:  \:  \:  \:  \rm{AB^2=AN^2+BN^2}

\rm{or,AB^2=(x_2-x_1)^2+(y_2-y_1)^2}

\rm\therefore AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

The Given question,

Find the distance of AG if A (4,4) and G (-1,-1).

Solution,

The given points are A(4,4) and G(-1,-1).

Then,

\rm{(x_1=4,y_1=4) and (x_2=-1,y_2=-1)}

We know that,

The distance formula,

\rm{AG=  \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}  }

\:  \:  \:  \:  \:  \:  \:  \:  =  \sqrt{ {( - 1 - 4)}^{2}  +  {( - 1  - 4)}^{2} }

\:  \:  \:  \:  \:  \:  \:  \:   =  \sqrt{ {( - 5)}^{2}  +  {( - 5)}^{2} }

\:  \:  \:  \:  \:  \:  \:  \:  =  \sqrt{25 + 25}

\:  \:  \:  \:  \:  \:  \:  \:   =  \sqrt{50}

\:  \:  \:  \:  \:  \:  \:  \:   =  \sqrt{(2)(25)}

\:  \:  \:  \:  \:  \:  \:  \:    =  \sqrt{(2)(5)(5)}

\:  \:  \:  \:  \:  \:  \:  \:    =  \sqrt{(2)( {5}^{2}) }

\rm  \:  \:  \:  \:  \:  \:  \:  \:  = 5  \sqrt{2}  \: units

Answered by:

\frak{\red{moonlight123429}}

DochEvi [55]2 years ago
3 0

{\qquad\qquad\huge\underline{{\sf Answer}}}

Let's solve ~

By using distance formula :

\qquad \sf  \dashrightarrow \:  \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2}  }

\qquad \sf  \dashrightarrow \:  \sqrt{(4 - ( - 1)) {}^{2} + (4 - ( - 1)) {}^{2}  }

\qquad \sf  \dashrightarrow \:  \sqrt{(4  + 1) {}^{2} + (4  + 1) {}^{2}  }

\qquad \sf  \dashrightarrow \:  \sqrt{2(5) {}^{2} }

\qquad \sf  \dashrightarrow \: 5 \sqrt{2 }\:  \: units

You might be interested in
Explain how you can approximate a cube root when the cube is not a perfect cube.
jenyasd209 [6]

Answer:

See below.

Step-by-step explanation:

It would take a long time to explain . There is a good method called Newton's method which involves graphs of the type

y = x^3 - n and applying calculus to produce cycles of approximation  until you'll get close to the required cubic root.

You'll find it on online videos.

5 0
3 years ago
Read 2 more answers
Factored form of 16m^4-121
AnnZ [28]

16m^4-121 =(4m^2-11)(4m^2+11)

8 0
3 years ago
P(red, blue, or green)
zhannawk [14.2K]
What is the question
4 0
4 years ago
A gym has three trainers, Aldo, Bertha, and Coco, who each have 1/3 of the new members. A person who trains with Aldo has a 60%
GarryVolchara [31]

Answer:

1/10

Step-by-step explanation:

P(a successful member

had Bertha as her trainer)  = P(Bertha being you trainer) x P(being successful if

                                                trained by Bertha)

                                             = 1/3 x 30/100

                                             = 30/300

                                             = 1/10

8 0
3 years ago
Suppose a normal distribution has a mean of 266 and a standard deviation of
pentagon [3]

Answer:C. 0.84

Step-by-step explanation:

Just took the quiz

6 0
3 years ago
Read 2 more answers
Other questions:
  • Please help me! I'll give brainliest!
    9·2 answers
  • Help me with question 4. and 5. for 100 points and brainlyest to the first answer
    6·2 answers
  • Joel made some muffins. He gave 1/4 of of the muffins to a neighbor. He took 3/8 of the muffins to school. What fraction of the
    9·1 answer
  • 4(-x+4)=12 <br> With steps
    13·2 answers
  • Derek has $20 to spend on used
    11·2 answers
  • Need help on this two column proof for geometry
    9·1 answer
  • I need help with this page
    7·1 answer
  • James wants to tile his floor using tiles in the shape of a trapezoid. To make the pattern a little more interesting he has deci
    12·1 answer
  • How many numbers of four different digits can be formed from the integers 0,2,4,5,6. ​
    14·2 answers
  • 2×+16=12(..........+...........)​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!