<p>i was taking the real sat II and had a problem with two of the questions. Can someone please help me out!!!</p>
<li>If P and Q are different points in a plane, the set of all points in the plane that are closer to P than to Q is : the answer is the region of the plane on one side of a line. ( i dont get the answer at all lol)</li>
<li>If n distinct planes intersect in a line and another line l intersects one of these places in a single point, what is the least number of these n planes that l could intersect? Ans: n - 1 </li>
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<p>Again i dont get how or why they got that answer. Also do u guys have any suggestions regarding texts that deal with these kind of planar stuff…</p>
<p>Thanks!!!</p>
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<li>Try a slightly different version of the question:
'If P and Q are different points in a plane, the set of all points in the plane that are the same distance from P and Q is ....?'</li>
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<p>You would draw a straight line connecting P and Q, and then draw a perpendicular line that bisects PQ. Every point on this perpendicular line is the same distance from P as it is from Q. So, if you moved off this perpendicular line towards P, whether the move was a teensy one or a large one, you would be closer to P than Q. Such a move would place you 'in the region of the plane on one side of the [perpendicular] line' .</p>
<p>QED .</p>
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<li>Think of the planes as pages in an open book, and 'intersecting line' as the spine of the book. If the new line intersects one of these planes in a single point, clearly it does not lie in that plane. Of the remaining (n-1) planes, it can miss at most one (if it happens to be exactly parallel to one of these planes). So the #planes that it intersects must be at least 1 [the one it intersects at a single point]
+ (n-1) [the remaining n-1 planes]
- 1 [ the plane it <em>may</em> be parallel to]</li>
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<p>i.e at least n - 1.</p>
<p>thanks a lot for your help!!!! It seems much clearer now :)</p>