Distance from Origin

orchidpsycho

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Sep 26, 2005
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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?
 
Hasn't your book covered the Distance Formula?

Eliz.
 
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)
 
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.
 
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?
 
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 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.
 
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
 
Whooooooh, You canna do that!!!
sqrt[(x1 - x2)2 + (y1 - y2)2]
sqrt[16 + 64]=
sqrt[80]
Do the addition first. PEMDAS
 
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.
 
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)
 
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
 
And "sqrt(20)" may be further simplified.

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