Distance from Origin

orchidpsycho

New member
Joined
Sep 26, 2005
Messages
41
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
Joined
Feb 4, 2004
Messages
15,943
Hasn't your book covered the Distance Formula?

Eliz.
 

orchidpsycho

New member
Joined
Sep 26, 2005
Messages
41
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
Joined
Feb 4, 2004
Messages
15,943
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
Joined
Sep 26, 2005
Messages
41
show distance from the origin are the same
 

orchidpsycho

New member
Joined
Sep 26, 2005
Messages
41
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
Joined
Feb 4, 2004
Messages
15,943
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
Joined
Sep 26, 2005
Messages
41
not sure what you mean?
 

stapel

Super Moderator
Staff member
Joined
Feb 4, 2004
Messages
15,943
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
Joined
Sep 26, 2005
Messages
41
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
Joined
Oct 8, 2003
Messages
1,904
Whooooooh, You canna do that!!!
sqrt[(x1 - x2)2 + (y1 - y2)2]
sqrt[16 + 64]=
sqrt[80]
Do the addition first. PEMDAS
 

orchidpsycho

New member
Joined
Sep 26, 2005
Messages
41
I get

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

sqt[100] = sqt[180]

like that?
 

stapel

Super Moderator
Staff member
Joined
Feb 4, 2004
Messages
15,943
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
Joined
Oct 8, 2003
Messages
1,904
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
Joined
Sep 26, 2005
Messages
41
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
Joined
Feb 4, 2004
Messages
15,943
And "sqrt(20)" may be further simplified.

Eliz.
 

orchidpsycho

New member
Joined
Sep 26, 2005
Messages
41
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
Joined
Oct 8, 2003
Messages
1,904
That's enough to answer the question but if you are going that far you should say 6sqrt(5)
------------------
Gene
 
Top