Wrong Answer in Barron(Math)

<p>Hi guys,</p>

<p>I am resolving Barron How to prepare for the SAT I found this question which has wrong answer I want to make sure though,because sometimes maybe I could have missed something.</p>

<p>If A(-1,1) and B(3,-1) are the endpoints of one side of square ABCD, what is the area of the square?</p>

<p>This question has two errors the first error is its stating that is a square the values are wrong
The height and width should be x;</p>

<p>Since both vectors has different x and different y we can conclude this should be the height and the width;</p>

<p>Height = 4; Width = 2; This should be a rectangle.</p>

<p>Also lets say we didn't conclude this we know that 3--1 = 4; so 4^2 = 16 and that answer is wrong; The actual answer is 20.</p>

<p>Is there something am I missing or is this question itself wrong ???</p>

<p>Look at the y coordinates, they are not the same. One is 1, while the other is -1.</p>

<p>The length of the segment is sqr(4^2 + 2^2)
That is the square root of 20, if you square that you get 20</p>

<p>The y coordinates should be 4 not 2,since the question states that its a square as I said.</p>

<p>If its a square all sides should be the same and should be as this picture.</p>

<p><a href="http://imageshack.us/photo/my-images/843/mathc.jpg/%5B/url%5D"&gt;http://imageshack.us/photo/my-images/843/mathc.jpg/&lt;/a&gt;&lt;/p>

<p>I'm too lazy to do math right now, but chances are that there's a typo in the book. Test prep books always have typos, I've yet to find one that doesn't. :)</p>

<p>Also, just did the problem and I got the area to be 20 as well</p>

<p>The two points they gave you are adjacent corners of the square, not opposite corners.</p>

<p>Looking at your picture, it appears you are visualizing the problem incorrectly.</p>

<p>Is this in the workbook or the complete prep book?</p>

<p>The 2 points given are one side of the square, so you cant compare the length and width. All that means is that the square is not level on the x/y coordinate plane. All you have to do is find the length of that side using the distance formula (d=sqr((y2-y1)^2+(x2-x1)^2), and then square that length because the area of a square is the length of one side squared.</p>

<p>It actually tells you in the question the the 2 points make one side of the square, so segment AB is on side, A and B are not opposite corners</p>

<p>What I don't understand is that the question gives us the vectors of the two points,since distance formula is just derived from pythogrean theorem we can get the difference between points which is weird to me coz the width is 4 and height 2 even though its a square.</p>

<p>They give you the coordinate of the 2 points, and those points are connected to form a segment, the point is that the square is diagonal, not flat. Your picture is incorrect</p>

<p>We are given Point A = (-1,1) and point B = (3,-1);</p>

<p>So if we follow these points and draw them on the graph we get this :-</p>

<p>ImageShack®</a> - Online Photo and Video Hosting</p>

<p>As you can see in the picture if we get the difference between the X2,X1 and
Y2,Y1 we would get 4,2 that is also given by distance formula.</p>

<p>Those two Points A,B form a diagonal it doesn't form a side.</p>

<p>Also a square should have all sides length are equal,which doesn't hold true here the width is of length 4 and the Height is of length 2.</p>

<p>The two points given do not form a diagonal of a quadrilateral, whatever that may be. The two points from one side of a square.</p>

<p>This image should clear the ambiguity:
<a href="http://img543.imageshack.us/img543/1295/74021064.png%5B/url%5D"&gt;http://img543.imageshack.us/img543/1295/74021064.png&lt;/a&gt;&lt;/p>

<p>^I see thats perfectly clear now thanks alot. </p>

<p>Also thanks to other people I just didn't visualize it right makes perfect sense now.</p>