# Distance from Origin

#### orchidpsycho

##### New member
Need help getting started on these 2 questions.

1. Show that the points(7,3) and (3,7) are the same distance from the origin.

2. Show that points A(-1,3), B(3,11), and C(5,15) are collinear by showing that d(A,B)+d(B,C)=d(A,C)

and help to get me started would be great. My book does'nt seem to cover these. The top one seems obvious when graphed but I assume they want and equation?

#### stapel

##### Super Moderator
Staff member
Hasn't your book covered the Distance Formula?

Eliz.

#### orchidpsycho

##### New member
it covers the distance formula. I tried this on #1

(3-7)^2+(7-3)^2
4^2+4^2
16+16
square root of 32

not sure what else to do.

The second one I am not sure how to set it up?

Thanks

Also is the origin (0,0)

#### stapel

##### Super Moderator
Staff member
Does the question ask you to find the distance between (7, 3) and (3, 7), or to show that their distances from the origin are the same?

Eliz.

#### orchidpsycho

##### New member
show distance from the origin are the same

#### orchidpsycho

##### New member
The second one I am starting like this?

d(A,B)

(3+1)^2 + (11-3)^2
(4)^2 + 8^2
16+64=80

d(B,C)

(5-3)^2 + (15-11)^2
(2)^2 + (4)^2
4+16=20

d(A,C)

(5+1)^2 + (15-3)^2
(6)^2 + (12)^2
36+144=180

does'nt add up. Not sure what I am doing wrong?

#### stapel

##### Super Moderator
Staff member
orchidpsycho said:
show distance from the origin are the same
1) So why are you finding the distance between the two points, instead of finding the distances between each of the points and the origin?

Eliz.

#### orchidpsycho

##### New member
not sure what you mean?

#### stapel

##### Super Moderator
Staff member
orchidpsycho said:
The second one...does'nt add up. Not sure what I am doing wrong?
Your book apparently contains a typo. The Distance Formula isn't just "(x<sub>1</sub> - x<sub>2</sub>)<sup>2</sup> + (y<sub>1</sub> - y<sub>2</sub>)<sup>2</sup>". It's supposed to contain a square root, as well:

. . . . .For points (x<sub>1</sub>, y<sub>1</sub>) and (x<sub>2</sub>, y<sub>2</sub>),
. . . . .the distance d between them is given by:

. . . . .sqrt[(x<sub>1</sub> - x<sub>2</sub>)<sup>2</sup> + (y<sub>1</sub> - y<sub>2</sub>)<sup>2</sup>]

Try that, and see what you get.

Eliz.

#### orchidpsycho

##### New member
d(A,B)

(3+1)^2 + (11-3)^2
(4)^2 + 8^2
sqt[16 + 64]= 4+8
=12

d(B,C)

(5-3)^2 + (15-11)^2
(2)^2 + (4)^2
sqt[4 + 16] = 2+4
=6

d(A,C)

(5+1)^2 + (15-3)^2
(6)^2 + (12)^2
sqt[36 + 144] = 6+12
=18

so
d(A,B) + d(B,C) = d(A,C)

12+6=18

Much better thanks my book does indeed have an error

#### Gene

##### Senior Member
Whooooooh, You canna do that!!!
sqrt[(x1 - x2)2 + (y1 - y2)2]
sqrt[16 + 64]=
sqrt[80]

#### orchidpsycho

##### New member
I get

sqt[80] + sqt[20] = sqt[180]

sqt[100] = sqt[180]

like that?

#### stapel

##### Super Moderator
Staff member
No.

. . . . .sqrt(x + y) DOES NOT EQUAL sqrt(x) + sqrt(y)

. . . . .Example:

. . . . .sqrt(9 + 16) = sqrt(25) = 5
. . . . .sqrt(9) + sqrt(16) = 3 + 4 = 7

Just follow the instructions. Work this exercise just like the Distance-Formula exercises shown in the book and done in class.

Eliz.

#### Gene

##### Senior Member
Nope, not yet. You better print out "order of operations" from the algebra lessons. That is PEMDAS. Sqrt is a type of exponent so it must be done before addition.
sqrt(80)+sqrt(20) IS NOT = sqrt(100)

#### orchidpsycho

##### New member
so

sqrt[80] + sqrt[20]

2(sqrt[20]) + sqrt[20]

3(sqrt[20])

and sqrt[180] also equals 3(sqrt[20])

not sure if thats how you format it?

Thanks for all the help and sorry so many questions

#### stapel

##### Super Moderator
Staff member
And "sqrt(20)" may be further simplified.

Eliz.

#### orchidpsycho

##### New member
3(sqrt[20])

and sqrt[180] also equals 3(sqrt[20])

3*2(sqrt[5]) = 3*2(srt[5])

6(sqrt[5]) = 6(sqrt[5])

#### Gene

##### Senior Member
That's enough to answer the question but if you are going that far you should say 6sqrt(5)
------------------
Gene