SOLUTION: 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

Question 337062: 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

Found 2 solutions by Fombitz, CharlesG2:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
The min and max distance between the points occur when they are collinear.
Maximum:P.....Q..R:PR=PQ+PR=5+2=7
Minimum:P..R...Q:PR=PQ-PR=5-2=3
If they are not collinear then the value for PR will lie between 3 and 7.
E) is the correct answer.

Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
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

distance PQ is the length of line PQ, distance QR is the length of line QR
distance PR is the length of line PR and is unknown
line PQ has length 5, line QR has length 2, line PR has length ?

these 3 lines form a triangle
PR has to be between the difference of PQ and QR AND the sum of PQ and QR, due to the Triangle Inequality Theorem (part of the properties of triangles)
PQ - QR = 5 - 2 = 3
PQ + QR = 5 + 2 = 7

3 < PR < 7
PR can not be 3 and PR can not be 7, UNLESS points are collinear (in a straight line)

(B) II only is answer, well if the 3 points are not collinear (in a straight line)

so answer is (E) I, II, and III
BUT case I and case III can only occur if the points are collinear

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