<p>Please help! This math question is from the Blue Official book/pg 778/Practice test 7/ Section 2. I would really appreciate an explaination of the answer</p>
<p>Q14. The three distinct points P,Q, and R lie on a line L; the four distinct points S,T,U,and V lie on a different line that is parallel to line L. What is the total number of different lines that can be drawn so that each line contains exactly two of the seven points. </p>
<p>ANSWER: 12 </p>
<p>Now, your probably thinking this is simple and straight forward, because it's:
(3 points on line L)x(4 points on line parallel to L). But I've taken into consideration that two points on the same line (e.g. P and Q) can form a line. So I wrote 17, and got that question wrong..</p>
<p>Does anyone know why the you don't count the lines you can make by connecting two dots on the same line???</p>
<p>if you count the lines linking the two points already on same line, then your line contains more than two points(see the last part of question). For instance, if you link P and Q, both on line L, then this line also passes through R. That's why you shouldn't count them.</p>
<p>Note carefully the wording in the question: "...so that each line contains exactly two of the seven points." I.e., not more than two, nor fewer than two, but exactly two. How many points does your line through P and Q contain?</p>
<p>if you connected P and Q, without having that PQ line going through ANY of the other points, it would actually be a segment, not a line. do you know what i mean?</p>
<p>Yeah, above is correct.
If you connect 2 points that are on the same line, it would encompass all other points on the line.</p>
<p>ex: _________________________
A b C d</p>
<p>Connecting A and B would make a line that connects c and d as well.</p>
<p>OH~ I get it now! thanks alot people!</p>