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Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Distance bw two points

In https://www.mathsisfun.com/algebra/distance-2-points.html I don't under stand this line The horizontal distance a is (xA − xB)

The vertical distance b is (yA − yB) plz tell how horizontal distance is xa-xb how

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Distance bw two points

I've copied the diagram and put in the coordinates for the point at the right angle.  This new point is directly below (Xa,Ya) so it has the same x coordinate, and on the same horizontal level as (Xb,Yb) so has the same y coordinate.  So it is the point (Xa,Yb)

Ya is clearly bigger than Yb so the vertical distance is Ya - Yb.

Xa is clearly bigger than Xb, so the horizontal distance is Xa - Xb.

I just think of these distances as the difference in Y coordinates and the difference in X coordinates.

In fact, it doesn't matter which is bigger out of the two coordinates.  Let's suppose the points are moved so that Xb is bigger than Xa.  Then Xa - Xb would be negative.  But when we use Pythagoras to square the distance, the sign changes to plus ( negative times negative = positive) so the result is the same.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Distance bw two points

How ya bigger than yb??? And how Xa is bigger than Xb,

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Distance bw two points

How ya bigger than yb??? And how Xa is bigger than Xb,

Ya is higher on the graph so it has a bigger y coordinate.  And Xa is further to the right.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Distance bw two points

Not understand ya bigger

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Distance bw two points

Oh dear.  We seem to be getting stuck on something that is not important.  I am going to start again:

Let's see this with numbers first:

Here we have 3 points A = (6,5);   B is (2,2);  and C is (6,2)

We will use Pythagoras' theorem to calculate the distance AB.

BC is a horizontal line, so its length can be found by calculating the difference in the x coordinates of the two points.

CA is a vertical line, so its length can be found by calculating the difference in the y coordinates of the two points.

Now the same with algebra:

In this diagram there are 3 points: A is (Xa,Ya);   B is (Xb,Yb);   and C is (Xa,Yb)

We will use Pythagoras' theorem to make a formula for the distance AB.

BC is a horizontal line, so its length can be found by calculating the difference in the x coordinates of the two points.

CA is a vertical line, so its length can be found by calculating the difference in the y coordinates of the two points.

So

and so

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Distance bw two points

BC is a horizontal line, so its length can be found by calculating the difference in the x coordinates of the two points. Why difference not adding why 6-2 and not 2-6

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Distance bw two points

In the Pythagoras formula it does not matter as (-4)^2 = (+4)^2 = 16

For the slope it does matter so you must be consistent:

If you start with a first then keep with a first throughout the formula.  Or start with b and keep with b first.

If you don't do this a positive slope will come out negative or a negative slope will appear to be positive.

I think a diagram will always help.  Line that slope like this /  have a positive slope.  \ is negative.

The distance will come out ok even if you switch a and b around carelessly.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Distance bw two points

Thx bob after this discusion I understand
and why we don't add Bc =6+2 why take difference and
2nd question
BC is a horizontal line, so its length can be found by calculating the difference in the x coordinates of the two     it's a horizontal why take difference what done in horizontal

Last edited by Zeeshan 01 (2016-11-07 20:11:00)

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Malik