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]
11 months 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]11 months 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
Book costs $5.25 plus sales tax. After sales tax, the book is $5.58. What is the sales tax rate?
Karolina [17]
5,25-5,58=0,33

The answer is $0,33
8 0
3 years ago
Read 2 more answers
Simplify the expression.<br><br> (–2)5<br><br><br> 16<br><br><br> –10<br><br><br> –32<br><br><br> 32
BigorU [14]

Answer:

the answer is -10

Step-by-step explanation:

Its basically multiplication

4 0
3 years ago
Simplify the following: (9x - 7) - (5x + 10)
lianna [129]
(9x - 7) - (5x + 10 )
2x - 15x
- 13x
7 0
3 years ago
Rosa recorded the height (in centimeters) of a pea plant over a ten day period for a science experiment.
notka56 [123]
I think that
The answer is A
y=2.0×(1.4^x)
4 0
3 years ago
Read 2 more answers
Marie has a small copy of Rene Magritte’s famous painting,The Schoolmaster.Her copy has dimensions 2 inches by 1.5 inches.The sc
alisha [4.7K]
The answer is 3 inches
6 0
3 years ago
Read 2 more answers
Other questions:
  • Find the slope of the line (-3,-2) and (3, 4)
    9·2 answers
  • The scatter plot shows the number of cds
    5·1 answer
  • Which pair of angles are supplmentary?
    11·2 answers
  • Explain why P(A|D) and P(D|A) from the table below are not equal.
    13·2 answers
  • A store is having a sale on walnuts and chocolate chips. For 9 pounds of walnuts and 7 pounds of chocolate chips, the total cost
    12·1 answer
  • Bobby's measuring cup holds 27 in3 of flour. He has enough flour to fill this measuring cup exactly 120 times. If his bread reci
    10·2 answers
  • Marbleslides: Lines
    11·1 answer
  • What is the volume of the cone below?
    7·1 answer
  • Your $440 gets 5.8% compounded annually for 8 years. What will your $440.00 be worth in<br> 8 years?
    8·1 answer
  • What is the place value?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!