SOLUTION: 1. If p, q, r are three points of a line and the coordinates of p and r are √3 and -√18, what is the coordinate of q given that pq = qr. 2. p, q, and r are three points of a l

Question 1194920: 1. If p, q, r are three points of a line and the coordinates of p and r are √3 and -√18, what is the coordinate of q given that pq = qr.
2. p, q, and r are three points of a line with coordinates x, y, and z in that order. If |x - z| + |z- y| = |x-y|, which point lies between the other two? Explain your answer
3. If p,q, and r are three points on a circle, can you identify which point is between the other two? Discuss.

Answer by ikleyn(52782) (Show Source): You can put this solution on YOUR website!
.

I will answer question 1, ONLY.

The problem hesitates to say that  p, q and r  are the points on a  line;


        so, they are not simply the points on the line. 
        As elements of a number line, they are the NUMBERS.




p = , r =   and pq = qr.


From  pq = qr  we have  pq = rq,  pq - rq = 0,  (p-r)q = 0.


Since p =/= r,  the factor in parentheses, (p-r), is different from zero.


THEREFORE,  (p-r)q = 0  implies  q= 0.


ANSWER.  From the given conditions, we derived  that  q = 0.

Solved.

/////////////

I do not touch questions 2 and 3, because everything is OBVIOUS there.

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A special note to the person who created this problem.

            Math problem should not hesitate to tell a truth.

            Otherwise, it is not a Math problem.

            Or a bad style to present a Math problem.

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