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This is in the 10 Real Sats book. I know the answer but I don’t understand how/why that is the answer.

Points P, Q, and R lie in a plane. If the distance between P and Q is 5 and the distance between Q and R is 2, which of the following could be the distance between P and R?

I. 3
II. 5
III. 7

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III

By yao on Wednesday, February 19, 2003 - 07:58 pm: Edit

(c) ??

By babadu on Wednesday, February 19, 2003 - 08:12 pm: Edit

think it's (e).
treat PQR as the vertices of a triangle and apply that rule about the lengths of the sides.
(5-2)<= PR <=(5+2)

i'm not sure but i think that's it

By Mrowry (Mrowry) on Wednesday, February 19, 2003 - 08:12 pm: Edit

Did you type the answers correctly? I thought it was II (5) and III (7).

By Mrowry (Mrowry) on Wednesday, February 19, 2003 - 08:13 pm: Edit

babadu: That's the theorem I was thinking of, but I thought the sum of the two sides had to be GREATER than the third, not greater or equal to.

By CalcMajor on Wednesday, February 19, 2003 - 08:13 pm: Edit

A. would be my guess! Distance between P and Q is 5. Distance between Q and R is 2. It's asking you the distance between P and R.

P -- Q = 5

Q -- R = 2

It's asking you the distance between, not total distance so it would be 5 - 2.

By Mrowry (Mrowry) on Wednesday, February 19, 2003 - 08:23 pm: Edit

Oh duh. I totally forgot about that scenario. It's definitely E, then.

By asdf on Wednesday, February 19, 2003 - 08:26 pm: Edit

im stupid, but e just sounds right to me

By babadu on Wednesday, February 19, 2003 - 08:36 pm: Edit

ooh wait a minute. sry bout that. i wrote the theorem incorrectly.

it's really PQ+QR >= PR.

the answer's still (e) but u should use this theorem for 3 points on a plane.

By sons on Wednesday, February 19, 2003 - 08:44 pm: Edit

u are all close minded...what if the point fell perpendicular or right next to the other point on the left side?

By sons on Wednesday, February 19, 2003 - 08:44 pm: Edit

sorry forgot the punchline, therefore its E

By Jason817 (Jason817) on Wednesday, February 19, 2003 - 08:50 pm: Edit

The answer is E. I know the sum of two sides is greater than the third but I don't see how that works in all three choices (in any of the three choices for that matter).

By Geoff on Wednesday, February 19, 2003 - 09:30 pm: Edit

the bottom line is that the max would be 7 (if the three points were in all on the same line). The min would be 3 (the points double back on themselves.) Thus, 3,5, and 7 all work, so it is e.

By Jason817 (Jason817) on Wednesday, February 19, 2003 - 09:46 pm: Edit

Ok that makes sense. But how does 5 work?

By babadu on Thursday, February 20, 2003 - 12:17 am: Edit

if the three points are in a straight line, 3 and 7 work. if the three points make a traingle than any number (x) greater than 3 and less than 7 work.

(5-2)<x<(5+2) <-- third side rule

By Geoff on Thursday, February 20, 2003 - 07:42 pm: Edit

yes, any real 3²x²7 would work for the reason above

By Jason817 (Jason817) on Thursday, February 20, 2003 - 07:45 pm: Edit

OK thanks. Got this one cleared up.

By your local mayor on Thursday, February 20, 2003 - 09:51 pm: Edit

E, think triangles.

By fgbyry on Sunday, February 23, 2003 - 10:42 pm: Edit

but if you think triangles then shouldn't it be B.... just 5.... b/c dont 2 sides have to be greater than the 3rd...if they're equal to it doesn't count?