help on today's SAT Q

Test Preparation SAT Preparation
1

<p>Four distinct lines lie in a plane, and exactly two of them are parallel. Which of the following could be the number of points where at least two of the lines intersect?</p>

<p>Three
Four
Five</p>

<p>A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III</p>

<p>I believe the answer is E but according to collegeboard, it is actually D. However, I can create 4 point of intersection if I place the 2 non parallel lines over the parallel ones in a nonparallel fashion. Can someone help explain?</p>

2

<p>No, it is not possible to create only 4 intersections. Check to see if you are missing anything. Think of it as a rule: All non-parallel lines MUST intersect. There are no exceptions. </p>

<p>You will always get 5 intersections, unless the intersection of the two non-parallel lines ALSO intersects with one of the parallel lines, in which case you get 3 intersections.</p>

3

<p>Only way you can have four points intersecting is if you have 2 pairs of parallel lines. The only choice is 3 and 5.</p>

4

<p>mmm! I see it now. Thank you!</p>

5

<p>yeah that was what i was thinking until i visualed it.</p>

<p>It cant be 4 because the two non parallel lines HAVE to intersect each other.</p>

6

<p>^ exactly. I didn't draw the lines out long enough to see them intersect. Haha! How very simple it actually is :)</p>

7

<p>this question had me for a second too, until i remembered the lines were in one plane. gotta read the question</p>

8

<p>In what setup can we get 3 interceptions if the lines continue forever?</p>

9

<p>Suppose that the 2 non-parallel lines intersect one another at the same point at which they both intersect one of the parallel lines.</p>