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
STatiana [176]
3 years ago
5

Find the distance between P(2, 8) and Q(5, 3).

Mathematics
1 answer:
swat323 years ago
8 0

Answer:

The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula

d = √  ((X2-X1)2+(Y2-Y1)2)

d = √ (5-2)2+(3-8)2

d = √ ((3)2+(-5)2)

d = √ (9+25)

d = √ 34

The distance between the points is 5.8309518948453

The midpoint of two points is given by the formula

Midpoint= ((X1+X2)/2,(Y1+Y2)/2)

Find the x value of the midpoint

Xm=(X1+X2)/2

Xm=(2+5)/2=3.5

Find the Y value of the midpoint

Ym=(Y1+Y2)/2

Ym=(8+3)/2=5.5

The midpoint is: (3.5,5.5)

Graphing the two points, midpoint and distance

P1 (2,8)

P2 (5,3)

Midpoint (3.5,5.5)

The length of the black line is the distance between the points (5.8309518948453)

Find the slope of the line connecting the two points

Slope =  (Y2-Y1)  =  (3-8)  =  (-5)  = -1.66666666666667

(X2-X1) (5-2) (3)

Find the equation of the line passing through the two points

The general equation for a straight line is

y = mx + b

Where m represents the slope of the line which we found in the previous step to be -1.66666666666667

y = -1.67x + b

We substitute x and y for the values from one of our points (2,8)

8 = -1.67×2 + b

8 = -3.33 + b

8--3.33 = b

11.33 = b

Knowing both b and m, we can contruct the equation of the line

y= -1.67x+ 11.33

X and Y intercepts

The x-intercept is a point on the graph where y is zero

Using the equation we found in the previous step and substituting zero for y

y= -1.67x+ 11.33

0= -1.67x+ 11.33

1.67x= 11.33

x= 11.33/1.67 = 6.80

The x intercept for this straight line is 6.80

The y-intercept is a point on the graph where x is zero

Using the equation we found in the previous step and substituting zero for x

y= -1.67×0+ 11.33

y= 11.33

The y intercept for this straight line is 6.80

References

refernce image showing the distance between two points on the xy plane

Step-by-step explanation:

You might be interested in
What’s the expression of this in simplest form
Ad libitum [116K]

Answer:

3/17

Step-by-step explanation:

3/4 divided by 4  1/4 is = to 3/4 divided by 17/4= 3/4 times 4/17 = 3/17

4 0
2 years ago
Read 2 more answers
I need help with 1-8 I have no idea how to do this so it you would break to down that I can understand that would be great
dem82 [27]

For these fractions, you need to find a number that can divide the numerator and denominator by the same number. It needs to be simplified down till it can't be simplified any more.


1. 1/9

2. 12/18

3. 5/6

4. 36/45

5. 5/8

6. 6/8

7. 10/12

8. 20/36

8 0
2 years ago
Read 2 more answers
At a high school, 14% of all students play a sport and 9% of all students play a
olga2289 [7]

Answer:

0.643

Step-by-step explanation:

Let, s = play a sport

c = participate in a club

P(s) = 0.14

P(s n c) = 0.09

probability that a student participates in

a club given that they also play a sport = P(c | s)

P(c | s) = P(c n s) / P(s)

P(c | s) = 0.09 / 0.14

P(c | s) = 0.64285

= 0.643

7 0
2 years ago
Which expression is equivalent to ? Assume.
nikdorinn [45]

Answer:

2. -2x^{8}y^{18}  

Step-by-step explanation:  

We have been given an expression \frac{10x^{6}y^{12}}{-5x^{-2}y^{-6}} and we are asked to find equivalent expression to our given expression.

Using fraction rule \frac{a}{-b} =-\frac{a}{b} we can write our expression as: -\frac{10x^{6}y^{12}}{5x^{-2}y^{-6}}. 

Upon dividing 10 by 5 we will get,

-\frac{2x^{6}y^{12}}{x^{-2}y^{-6}}      

Upon using exponent property for quotient (\frac{a^{m}}{a^{n}} =a^{(m-n)}) we will get,  

-\frac{2x^{6}y^{12}}{x^{-2}y^{-6}}=-2x^{(6--2)}y^{(12--6)}    

-2x^{(6+2)}y^{(12+6)}

-2x^{8}y^{18}        

Therefore, our expression simplifies as -2x^{8}y^{18} and 2nd option is the correct choice.



6 0
3 years ago
Read 2 more answers
If f(x)=x-7 and g(x)=x^3, what is G(f(x))?
lesya692 [45]
Replace the 'x' in the formula for g(x) by f(x):-

g(f(x)) =  (x-7)^3

Its D
8 0
3 years ago
Read 2 more answers
Other questions:
  • What characteristics make Ur an advanced city?
    5·1 answer
  • Which of the following best describes the term induction?
    12·1 answer
  • Renita analyzed two dot plots showing the snowfall during the winter months for City A and for City B. She found that the
    11·2 answers
  • Please help me on this.
    8·1 answer
  • I need this answered desprately!!
    8·1 answer
  • Add.<br> (6v^2+6v+2)+(5v+7)
    8·1 answer
  • What is 10% on sale for sale on $ 37.89
    11·1 answer
  • What is the slope of a graph?​
    8·2 answers
  • The formula for the volume of a rectangular prism is V = lwh. Which is the equivalent equation solved for h? StartFraction V Ove
    11·2 answers
  • How do i draw 5/6 x 1/3 on an area model???????<br>​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!