Find the distance between the set of points. (-4, 5) and (4, 0) Question 2 options: 3.32 9.4 4.58 89

Step-by-step explanation I have drawn a graph in which there are two points

p

1

(

x

1

,

y

1

)

and

p

2

(

x

2

,

y

2

)

.

We can easily say that

¯¯¯¯¯¯

O

D

=

x

1

;

¯¯¯¯¯¯

O

E

=

x

2

;

¯¯¯¯¯¯

A

D

=

y

1

;

¯¯¯¯¯¯

E

B

=

y

2

We also have a rectangle

□

O

C

E

D

. So,

¯¯¯¯¯¯

A

C

=

¯¯¯¯¯¯

D

E

and

¯¯¯¯¯¯

A

D

=

¯¯¯¯¯¯

C

E

Now,

¯¯¯¯¯¯

A

C

=

¯¯¯¯¯¯

D

E

=

¯¯¯¯¯¯

O

E

−

¯¯¯¯¯¯

O

D

=

(

x

2

−

x

1

)

¯¯¯¯¯¯

B

C

=

¯¯¯¯¯¯

B

E

−

¯¯¯¯¯¯

C

E

=

¯¯¯¯¯¯

B

E

−

¯¯¯¯¯¯

A

D

=

(

y

2

−

y

1

)

With the help of Pythagorean theorem,

¯¯¯¯¯¯

A

B

2

=

¯¯¯¯¯¯

B

C

2

+

¯¯¯¯¯¯

A

C

2

¯¯¯¯¯¯

A

B

2

=

(

x

2

−

x

1

)

2

+

(

y

2

−

y

1

)

2

¯¯¯¯¯¯

A

B

=

√

(

x

2

−

x

1

)

2

+

(

y

2

−

y

1

)

2

N.B:- As it is a square value , you may take

(

x

1

−

x

2

)

or,

(

x

2

−

x

1

)

. I mean you have to take difference.That's

(

x

1

~

x

2

)

So, the required formula is proved that

If the distance between two points

p

1

(

x

1

,

y

1

)

and

p

2

(

x

2

,

y

2

)

is

r

,

then,  

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

∣

∣

∣

r

=

√

(

x

1

−

x

2

)

2

+

(

y

1

−

y

2

)

2

∣

∣

∣

−−−−−−−−−−−−−−−−−−−−−−−−−−−

Hope it helps...

Thank you...

Sunayan S ·  1 · Apr 6 2018

How do you find the distance when given two coordinate points?

Distance Formula

The distance

D

between two points

(

x

1

,

y

1

)

and

(

x

2

,

y

2

)

can be found by

D

=

√

(

x

2

−

x

1

)

2

+

(

y

2

−

y

1

)

2

Example

Find the distance between the points

(

1

,

−

2

)

and

(

5

,

1

)

.

Let

(

x

1

,

y

1

)

=

(

1

,

−

2

)

and

(

x

2

,

y

2

)

=

(

5

,

1

)

.

By Distance Formula above,

D

=

√

(

5

−

1

)

2

+

[

1

−

(

−

2

)

]

2

=

√

16

+

9

=

√

25

=

5

I hope that this was helpful.:

w'x is 0.

hope it