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 furniture company increased the item fee to $0.75 per pound.Mr.Jackson buys a piece of furniture that weighs 8 pounds.He thi
Vinil7 [7]
Mr.Jackson is incorrect because 0.75 is per pound it's not whats added onto 8 pounds
5 0
3 years ago
Write an equation that you can use to find the value of x. Perimeter of triangle: 16 in. An equation that you can use is 16=
Ad libitum [116K]

Answer

16=3x

Step-by-step explanation:

Each side has x

there is 3 sides

so 3x will equal 16.

Hope this helped!

5 0
3 years ago
How many x -intercepts does the parabola whose function is f(x)=3 x 2 +4x+4
artcher [175]

Answer:

They are none x- intercepts on the parabola. To find the x-intercept, substitute in 0 for y and solve for x.

3 0
3 years ago
Read 2 more answers
The perimeter, P, of a rectangle is found using the formula P = 2l + 2w, where l is the length of the rectangle and w is the wid
pogonyaev

Answer:

(P - 2l)/2

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Please answer these questions asap please!!! Thank you!
Len [333]

Answer:

a= 1%

b= 0.1%

c= 0.1875% probably have to round

Step-by-step explanation:

a= 2/2= 1

B= 1/10=0.1

c= 1.5/8= 0.1875

6 0
3 years ago
Other questions:
  • I don’t understand!! Please someone help ASAP !
    14·1 answer
  • A swimming pool is 15 feet wide, 50 feet long and has an average depth of 5 feet. How many cubic feet of water will it hold.
    13·2 answers
  • First, a 90 percent confidence interval is constructed from a sample size of 100. Then, for the same identical data, a 92 percen
    5·1 answer
  • Expressed in simplified radical form what is the value of √r-√16r when r=2
    7·1 answer
  • An individual is hosting a cookout for the kick ball team. The individual wants to have two hot dogs for each guest, and 6 extra
    7·1 answer
  • Classify the system of equations.
    13·1 answer
  • The straight line L passes through the points (0, 12) and (10, 4). <br> Find an equation for L.
    12·1 answer
  • 22a) PLEASE HELP BEST ANSWER BRAINLIEST
    10·1 answer
  • A school newspaper says that 6% of the students surveyed, can wiggle their ears. How many students were surveyed ? If a school h
    11·1 answer
  • Simplify (8z - 10) ÷ (-2) + 5(z - 1).<br> OZ<br> OZ-1<br> Oz-2
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!