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
(-3)*(-5) =
vlabodo [156]

Answer:

9×5=45

Step-by-step explanation:

hope it helps and use brainly it never lies

8 0
3 years ago
Read 2 more answers
Walter is fencing in his backyard for every 20 fence boards he needs 3 metal posts how many metal posts will he need for 300 fen
laila [671]

Answer:

15 metal post

Step-by-step explanation:

all you have to do is divide 20 into 300

4 0
3 years ago
What is the product of (x 1)^2?
Viktor [21]
The product of (x1)^2 is 20
6 0
3 years ago
A hand-operated conduit bender with a shoe for bending 1-inch EMT can also be used to bend
Lunna [17]
1/2 inch EMT.........................
5 0
3 years ago
I need to know how to write an equation whose solution is x=3.5 but i don't know how
inysia [295]

Answer:

2x+5=12

Step by-step explanation:

2x+5=12

Subtract 5

2x=7

Divide each side by 2

x=3.5

7 0
3 years ago
Other questions:
  • Divide $28 in the ratio 5:2:7.
    14·1 answer
  • Which sentence explains the correct first step in the solution of this equation? 4 • (x – 3) = 9
    10·2 answers
  • Two number cubes are rolled. What is the probability that the sum of the numbers rolled is either a 7 or an 11?
    10·1 answer
  • Simplify square root of 484
    8·1 answer
  • Ducks unlimited helps sample duck species across the united states. Samples from one particular location for the last two years
    6·2 answers
  • A Luxury of Furniture at a store sells couches for $4,000,Reclining Chairs for $2,040 and loveseats for $2,800. This Luxury line
    14·1 answer
  • HELP PLS- I WILL GIVE BRAINEST
    9·1 answer
  • Using the formula below, find F, when f = 1000 and r = 8
    5·2 answers
  • Please help me!!! I'll give you 40 points.<br>construct the bisector of the following figures​
    12·2 answers
  • The Kansas City Chiefs are trying to figure out if there is a relationship between the number of passes thrown by Quarterback Pa
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!