Can someone explain how to answer this ?

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1

<p>I get how the answer can be five points, but I don't get how it can be three points. Can someone explain it please?</p>

<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>

<ol>
<li><p>Three</p></li>
<li><p>Four</p>

<ol>
<li>Five</li>
</ol>

<p>(A) 1 only
(B) 3 only
(C) 1 and Roman numeral 2 only
(D) 1 and 3 only
(E) 1, 2, and 3
Since exactly two of the four lines are parallel, the other two lines are not parallel. If the two non-parallel lines intersect at a point that is not on either one of the parallel lines, then the configuration of lines will give a total of 5 points of intersection. (The best way to verify this is by drawing the two parallel lines and then putting in the other two lines.) If, on the other hand, the two non-parallel lines intersect at a point that is on one of the parallel lines, then there will be a total of 3 points of intersection in the figure. (Again, a sketch is the best way to verify this.) Any arrangement of the four lines will again yield either 3 or 5 points of intersection. Since you can’t obtain four points of intersection, the correct answer is Roman numeral 1 and Roman numeral 3 only.</p></li>
</ol>

2

<p>If the two lines that are not parallel intersect at exactly on one of the parallel ones. So it looks like a triangle</p>

3

<p>If three lines intersect at one point, then three is correct. It does look like a triangle. Let’s say there are two vertical parallel lines. Then a horizontal line in the middle. The 4th (diagonal) line intersects where the straight and horizontal line intersect (and also, the 4th line intersects with the second straight line).
The first intersection of lines is between the veritcal and horizontal lines.
The second intersection of lines is between the same vertical line and the diagonal line.
The third intersection of lines is among the second vertical line, horizontal line, and diagonal line.
I hope this helped</p>