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
Natasha2012 [34]
1 year ago
9

Find the distance from point A(−9,−3) to the line y = x−6. Round your answer to the nearest tenth.

Mathematics
1 answer:
Vladimir79 [104]1 year ago
8 0

The distance from point A(−9,−3) to the line y = x−6 is 8.5 units

<u>What is slope ?</u>

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

step 1

Find the slope of the perpendicular line to the given line

y=x-6 ---> given line

The slope is m=1

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

m1*m2 = -1

we have

m1=1

substitute

(1)*m2 = -1

so

m2 = -1

step 2

Find the equation of the perpendicular line to the given line

The equation in point slope form is

y-y1=m(x-x1)

we have

m=-1

(x1,y1)=(−9,−3)

substitute

y+3=-1(x+9)--> equation in point slope form

y+3= -x-9

y= -x-12---> equation in slope intercept form

step 3

Find the intersection point between the given line and the perpendicular line to the given line

we have the system of equations

y = x−6.

y= -x-12

Solve the system by graphing

The intersection point is (-3,-9)

see the attached figure

step 4

we know that

The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6

the formula to calculate the distance between two points is equal to

d=√[(y2-y1)² + (x2-x1)²]

substitute the values

d=√[(-9+3)² + (-3+9)²]

d= √72 units

simplify

d= 6√2 = 8.5 units

To learn more about the slope from the given link

brainly.com/question/16949303

#SPJ1

You might be interested in
The Statue of Liberty is about 300 feet tall and about 30 feet wide. The town of Unionville is building a smaller model for thei
hichkok12 [17]
It’s dividing by a factor of 10. So 30 divided by 10=3. You then do the same thing for the height. 300 divided by 10=30. The answer is 30.
5 0
3 years ago
A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid.
CaHeK987 [17]
Area of the Base = 6 * side^2 / 4 * tan (180/6)
Area of the Base = 6 * 16 / 4 * 0.57735
Area of the Base = 96 / <span> <span> <span> 2.3094 </span> </span> </span>
Area of the Base = <span> <span> <span> 41.5692387633 </span> </span> </span>

Area of 1 Face = 2 * 6 = 12
Area of 6 Faces = 72

<span> <span> Total Area = 41.5692387633 </span> + 72</span>
Total Area = 113<span>.5692387633</span>


6 0
3 years ago
Read 2 more answers
What is the equivalent decimal form for<br> 2/40?
Lelechka [254]

Answer:

decimal form: 0.05

Step-by-step explanation:

To find decimals divide them, so 2 divided by 40 is 0.05.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. thank you and have a nice day!

4 0
3 years ago
Read 2 more answers
2g + h =2<br>g -h= -5<br><br>find g and h step by step explanation​
wel

Answer:

Step-by-step explanation:

2g + h = 2 --------------(I)

g - h = -5------------(II)

   g = -5 + h

Plugin g = -5 + h in equation (I)

  2(-5 + h) + h = 2              {Distributive property:a(b+c) = a*b +a*c}

(-5)*2 + h *2 + h= 2

-10 + 2h  + h    = 2

             3h = 2 + 10

       3h = 12

         h = 12/3

h = 4

Substitute h= 6 in equation (I)  

2g + 4 = 2

    2g = 2 - 4

    2g = -2

      g = -2/2

g = -1

6 0
3 years ago
Find the area of the figure.
mariarad [96]

Answer:25

Step-by-step explanation:Count all the wholes then put all the halves and there is 25

5 0
3 years ago
Read 2 more answers
Other questions:
  • Rational or irrational ?
    5·1 answer
  • Explain answer??????????????????
    8·1 answer
  • What's the answer???
    6·1 answer
  • Help fast please!!! <br> Find the values of x and y.
    9·2 answers
  • Simplify 5/8-(-7/2)
    10·2 answers
  • The price of a toy usually costing £50 is increases to £65<br> work out the percentage increase
    9·2 answers
  • 70 students per 2 teachers
    8·2 answers
  • Given the formula for the perimeter of a rectangle where I represents the length and w represents the width 2(l+w)
    6·1 answer
  • A group of friends decides to go to the local bowling alley. They can rent the lane for 1 hour at a cost of $ 20 and the shoes a
    8·1 answer
  • Can someone please help I will give you 30 points and brainliest if the answer is right also no links please
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!