pg 776 / #8 / Math BLUE BOOK

Test Preparation SAT Preparation
1

<p>I already solved it for you guys in case you guys need help.
Here’s the problem:
pg 776 / #8</p>

<p>Rectangle ABCD lies in the xy-coordinate plane so that its sides are not parallel to the axes. What is the product of the slopes of all four sides of rectangle ABCD?</p>

<p>a. -2
b. -1
c. 0
d. 1
e. 2</p>

<hr>

<p>Solution:</p>

<li>First, we must draw up what the rectangle looks like on the graph. Since all sides are not parallel to any of the axis, our rectangle looks like this:</li>
</ol>

<p><a href=“http://img250.imageshack.us/img250/4838/rectangleld6.jpg[/url]”>http://img250.imageshack.us/img250/4838/rectangleld6.jpg</a></p>

<p>A rectangle has four ninety degree angles, as you know (Side note: unfortunately, our minds sometimes, when we do the SAT, don’t think about that. The SAT is quite good at writing problems down that makes you stumped about a topic that you might already know, and would have known if you were able to extricate the problem’s real meaning, but instead, your mind is left confused by the problem)</p>

<li>Our next step is to pick the numbers of slope. Now, remember when I talked about the ninety degree angles? Any line perpendicular to a line in a graph is always the inverse of the latter. Therefore, we have two equal sides, and slopes, perpendicular to two different, yet equal, sides, and slopes, because the shape is a rectangle. IT IS IMPORTANT THAT ONE SLOPE IS THE INVERSE OF ANOTHER IN THIS PROBLEM!</li>
</ol>

<p>As for our slopes, I will pick 1/2 for the 2 sides that are going up and I will pick -2/1 (inverse b/c of perpendicular) for the 2 sides that are going down.</p>

<li>Now we multiply our slopes. </li>
</ol>

<p>4 sides = 4 slopes, therefore:</p>

<p>(1/2 * 1/2) * (-2/1 * -2/1) = 1</p>

<p>The answer is d, 1. </p>

<p>Here’s a drawing for those who are lost:
<a href=“http://img399.imageshack.us/img399/9753/rectangle2vt5.jpg[/url]”>http://img399.imageshack.us/img399/9753/rectangle2vt5.jpg</a></p>

<p>I hoped I answered some questions.</p>

2

<p>um did anyone ask for this?</p>

<p>you are weird</p>

3

<p>No, it was in case it was asked.</p>

4

<p>Great explanation, Avex! Thanks.</p>

5

<p>You have no life Avex. Why would you waste your time?</p>

6

<p>thepack888: Teaching others is the best way to learn. So there was no better way to use his time.</p>

7

<p>thnxs 4 posting this up, Avex. i see some people dont appreciate what they're given.</p>

8

<p>Easier way:
the product of 2 perpendicular lines is -1, since there are 4, sqaure it, which yields 1.</p>

9

<p>^ That method is the most efficient.Sensei will now enlighten you with his wisdom, remember this and you will go far my student. </p>

<p>The perpendicular line to a line is the NEGATIVE RECIPROCAL (flip it and negate it) of the original line. They are thus INVERSES of each other thus they are equal to -1. As anthimmy mentioned, there are 2, so thats -1 x -1 = 1.</p>