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
Makovka662 [10]
2 years ago
15

Find the distance between (−4, −3) and (−2, 0). Round your answer to the nearest tenth.

Mathematics
1 answer:
andrew-mc [135]2 years ago
4 0

Answer:Given the two points you entered of (-4, -3) and (-2, 0), we need to calculate 8 items:

Item 1: Calculate the slope and point-slope form:

Slope (m)  =   y2 - y1

  x2 - x1

Slope (m)  =   0 - -3

  -2 - -4

Slope (m)  =   3

  2

Calculate the point-slope form using the formula below:

y - y1 = m(x - x1)

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

Item 2: Calculate the line equation that both points lie on.

The standard equation of a line is y = mx + b where m is our slope, x and y are points on the line, and b is a constant.

Rearranging that equation to solve for b, we get b = y - mx. Using the first point that you entered = (-4, -3) and the slope (m) = 3/2 that we calculated, let's plug in those values and evaluate:

b = -3 - (3/2 * -4)

b = -3 - (-12/2)

b  =   -6

  2

-

 

-12

2

b  =   6

  2

This fraction is not reduced. Using our GCF Calculator, we see that the top and bottom of the fraction can be reduced by 6

Our reduced fraction is:

1

0.33333333333333

Now that we have calculated (m) and (b), we have the items we need for our standard line equation:

y = 3/2x + 3

Item 3: Calculate the distance between the 2 points you entered.

Distance = Square Root((x2 - x1)2 + (y2 - y1)2)

Distance = Square Root((-2 - -4)2 + (0 - -3)2)

Distance = Square Root((22 + 32))

Distance = √(4 + 9)

Distance = √13

Distance = 3.6056

Item 4: Calculate the Midpoint between the 2 points you entered. Midpoint is denoted as follows:

Midpoint =

 

x2 + x1

2

 

,

y2 + y1

2

Midpoint =

 

-4 + -2

2

 

,

-3 + 0

2

Midpoint =

 

-6

2

 

,

-3

2

Midpoint = (-3, -3/2)

Item 5: Form a right triangle and calculate the 2 remaining angles using our 2 points:

Using our 2 points, we form a right triangle by plotting a 3rd point (-2,-3)

Our first triangle side = -2 - -4 = 2

Our second triangle side = 0 - -3 = 3

Using the slope we calculated, Tan(Angle1) = 1.5

Angle1 = Atan(1.5)

Angle1 = 56.3099°

Since we have a right triangle, we only have 90 degrees left, so Angle2 = 90 - 56.3099° = 33.6901

Item 6:  Calculate the y intercept of our line equation

The y intercept is found by setting x = 0 in the line equation y = 3/2x + 3

y = 3/2(0) + 3

y = 3

Item 7: Determine the parametric equations for the line determined by (-4, -3) and (-2, 0)

Parametric equations are written in the form (x,y) = (x0,y0) + t(b,-a)

Plugging in our numbers, we get

(x,y) = (-4,-3) + t(-2 - -4,0 - -3)

(x,y) = (-4,-3) + t(2,3)

x = -4 + 2t

y = -3 + 3t

Calculate Symmetric Equations:

x - x0

z

 

y - y0

b

Plugging in our numbers, we get:

x - -4

2

 

y - -3

3

Step-by-step explanation:

You might be interested in
A football coach set a goal of keeping opposing teams to an average of less than 200 yard. of total offense each game. After thr
faust18 [17]
(701+y)/(3+1)<200

(701+y)/4<200

701+y<800

y<99

So the most yards they can allow in the next game is 98 yards
6 0
3 years ago
The wave occurred in<br><br> in<br> It reached 1,720 feet.
Usimov [2.4K]
It occurred in July 9, 1958. It occurred in Lituya Bay, Alaska.
6 0
2 years ago
Can someone help me with this math homework please!
TEA [102]

Answer:i dont know

Step-by-step explanation:

4 0
3 years ago
7*6=42 is that and factor
Salsk061 [2.6K]

yes 7*6=42 is a factor


7 0
3 years ago
What is the answer to the problem <br><br><img src="https://tex.z-dn.net/?f=%28x%20%7B3%7D%29%5E%7B3%7D%20%3D%20x%5En" id="TexFo
11Alexandr11 [23.1K]
Solve for x:
x^9 = n x

Subtract n x from both sides:
x^9 - n x = 0

Factor x and constant terms from the left hand side:
-x (n - x^8) = 0

Multiply both sides by -1:
x (n - x^8) = 0

Split into two equations:
x = 0 or n - x^8 = 0

Subtract n from both sides:
x = 0 or -x^8 = -n

Multiply both sides by -1:
x = 0 or x^8 = n

Taking 8^th roots gives n^(1/8) times the 8^th roots of unity:
Answer: x = 0 or x = -n^(1/8) or x = -i n^(1/8) or x = i n^(1/8) or x = n^(1/8) or x = -(-1)^(1/4) n^(1/8) or x = (-1)^(1/4) n^(1/8) or x = -(-1)^(3/4) n^(1/8) or x = (-1)^(3/4) n^(1/8)
3 0
3 years ago
Other questions:
  • Solve this system:<br><br> 2x+5y+z=3<br> x-3y+2z=2<br> -x+2y-3z=-7
    5·1 answer
  • 60 cars to 24 cars what is the percent of change can you tell me answer and explain thanks
    12·1 answer
  • 3. What is the distance from (−4, 0) to (2, 5)? Round your answer to the nearest hundredth. (4 points)
    15·1 answer
  • At how many different lines of reflection can you reflect a square onto itself?
    13·1 answer
  • A property insurance policy is issued at a total cost of $2,540 for 6 months. If the insurance company offers a one-time $50 reb
    12·1 answer
  • According to a survey of 500, the mean income before taxes of consumer units (i.e., households) inthe U.S. was $60,533 with a st
    11·1 answer
  • Find the eccentricity of the ellipse<br> 4x^2 +16y^2 +32x-32y+16=0
    12·1 answer
  • What is the slope of the line? Type fractions as y/x).
    15·1 answer
  • A square is cut from a piece of plywood. How can you determine whether the quadrilateral cut out of the plywood is indeed a squa
    12·2 answers
  • I need these questions done triginometry
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!