P, D, and R are collinear, PQ=17, PR=5. What are the possible lengths of QR

Answer 1

P, D, and R are collinear, PQ=17, PR=5. What are the possible lengths of QR

I assume by "D" you mean "Q". Since P, Q, R are collinear, they are all points on the same line. Imagine a line, PRQ, as follows:

<--------------P------------R---------------------Q------------->

Since PQ is 17, PR is 5, and R lies between PQ, then we can subtract the length of PR from the length of PQ to get one possible length of QR.

|QR| = |PQ| - |PR| = 17 - 5 = 12

So, one possible length of QR is 12.

Consider another possible line, QPR, as follows:

<------Q---------------------P-----------R---------->

In this case, the length of PQ can be added to the length of PR to find the length of QR.

|QR| = |PQ| + |PR| = 17 + 5 = 22

So, another possible length of QR is 22.

Note that any other possible lines with points P, Q, R are not possible because of the lengths given for PQ and PR. Thus, the possible lengths of QR are 12 and 22.