I have a test today and dont understand this one kind of problem. Help?

Question

I need to understand how to find the difference from two points mathematically. I have this equation, but I'm not sure how to use it. It looks like this: (x2-x1)^2 + (y2-y1)^2. Can some one help me with an example. On the reveiw it has one of these for (-2,3) (6,7). I have another question and you can go for that one too. Its in this section.

Answer 1

Hi,

The formula is a derivation of Pythagora's Theorem. Your points (-2, 3) and (6, 7) on the cartesian plane using ordinates from (x, y) so, (x1, y1) and (x2, y2) etc relate to your formula:

D^2=(x2-x1)^2+(y2-y1)^2

which gives using (-2, 3) (6, 7)

D^2 = (6--2)^2+(7-3)^2
= 8^2+4^2
= 64 + 16
= sqrt (80)
= some decimal on your calculator

Hope this helps...

Answer 2

Actually, the equation for the *distance* between 2 points is
d = √[(x2 - x1)² + (y2 - y1)²]

We are given points
(-2,3)
(6,7)
which correspond to
(x1,y1)
(x2,y2)

We have
x1 = -2
x2 = 6
y1 = 3
y2 = 7

You can now substitute these values into the distance formula:
d = √[(6 - {-2})² + (7 - 3)²]

Simplify as follows:
d = √[(6 + 2)² + (7 - 3)²]

d = √(8² + 4²)
d = 4√(4 + 1)
d = 4√5

Therefore, the distance between (-2,3) and (6,7) is 4√5.

^_^

Answer 3

You just have to substitute x1, x2, y1, and y2 with the coordinates of the points you have, which are in the form (x1, y1) and (x2, y2). So in your example, with points A(-2,3) and B(6,7):
x1 = -2 and y1 = 3
x2 = 6 and y2 = 7
Now when you substitute these values in the formula you'll get:
(6 + 2)^2 + (7 - 3)^2 = (8)^2 + (4)^2 = 64 + 16 = 80
The answer we just got is the square of the distance AB, so the actual line segement AB is equal to the square root of 80, or about 8.94.

Answer 4

The equation is equivalent to the Pythagorean theorem a^2 + b^2 = c^2. Given the two points plotted (-2,3) and (6,7) a line can be plotted between them, in this case it will be a diagonal. (You can do this on graph paper, it may help you understand what I am about to explain.)

Now plot a line that extends from (-2,3) to (6,3), basically a straight line between the X coordinates.

Now drop another line from (6,7) to (6,3) creating a line between the Y coordinates. You will have formed a right triangle. This is the shape on which the equation is based. (I wish I could accompany this with illustrations it would be so much easier to follow.)

Your original line is the c^2 length in the formula above.

So, if we substitute your values for X and Y we get.

a^2 + b^2 = c^2

(6 - (-2))^2 + (7-3)^2 = c^2

8^2 + 4^2 = c^2

64 + 16 = c^2

80 = c^2

c = square root of 80

Answer 5

the co-ordinates of a point are (x,y).Therefore take x1=-2 and x2=6.Also take y1=3 and y2=7.You then substitute the values into equation u have
(6--2)^2+(7-3)^2
(6+2)^2+(7-3)^2
(8)^2 + (4)^2
64+16=80
Then u find the square root of 80 which is approximately 8.944

Answer 6

(x2-x1)^2 + (y2-y1)^2
the x and y are the x and y co ords that are given to you. You take the points you are giving and just plug them in.

so with the sample the numbers that corespond in the formula are above the form values
(-2, 3 ) (6 , 7 )
x1 y1 x2 y2

so plugged in it would be
(x2-x1)^2 + (y2-y1)^2 in this problem is: (6- (-2))^2+ (7-3)^2
same as (6+2)^2 + (7-3)^2
evaluates down to
8^2 + 4^2

So I think thats right, but its been 9 years.

Answer 7

consider to points
1. (x1, y1)
2. (x2, y2)

U have find the distance between two points OK?

distance between two lines formula

d= sqrt((x2-x1)^2 +(y2-y1)^2) {using Pythagoras theorem}

so substitute these values

d= sqrt((6-(-2))^2+(7-3)^2)

d= sqrt(8^2+4^2)

d= 8.9443

Answer 8

fill in the x cordinates in the first part then the y's in the secodn part. so it would be done like this
(6--2)^2+(7-3)^2=
(6+2)^2+(7-3)^2=
8^2+4^2=
64+16=
square root of80=8.94
.

X2 is the second x coordinate X1 isthe first X coordinate. same thing for the Y

Answer 9

This is like joining the two points.
ex. as U say,(-2,3) & (6,7)
Now think of a trangle of legs 3,4,& 5 of length. so the 3^2+4^2=5^2
isnt it?Then if we take x coordinate diference & take Y coordinate diference & take its squqre value & like in3 4 5 case You can get the distance between the points by takin the root of the answer.

:)