<p>In the xy-plane, three of the vertices of a square are (0,0), (0,3), and (3,0). If the square is reflected about the line y = -x, which of the following is one vertex of the resulting square? Why is it flipped diagonally rather than across the x axis?</p>
<p>In triangle MPG, the measure of angle M is 30 degrees and the measure of Q is 45 degrees. What is the length of segment MQ if MP is 10?</p>
<p>z= x - y + 4
z = y - w - 3
z = w - x + 5
Based on the system of eqs above, what is the value of z?</p>
<p>To do the last one, just add them. You get:</p>
<p>3z = 6
z = 2</p>
<p>heh thanks.. I was trying to solve for this and plug it into that and all of this cra p.. yeah it didn't turn out very well...</p>
<p>I was trying to do the second one but... ***? There is a mention of Q there, but the triangle is named MPG. Am I missing something here? Or is there another segment? If there is, the question is unanswerable as posed; please provide a diagram.</p>
<p>typo it is suppose to be Q</p>
<p>Given the above information, my first thought would be to use the law of sines to get a fast answer. The law of sines is trigonometry, yes, but it's easy to memorize and all you have to do is plug in buttons in your calculator. The law states:</p>
<p>a/sin(A) = b/sin(B) = c/sin(C)</p>
<p>Firstly we find the angle on p, which is 105 degrees.</p>
<p>We therefore have:</p>
<p>10 / sin(45) = MP / sin(105)</p>
<p>Solve for MP.</p>
<p>10sin (105) / sin (45) = MP</p>
<p>Plug in numbers into your calculator and make sure it is in degree mode. You should get:</p>
<p>13.66025404...</p>
<p>Is that the correct answer?</p>
<p>how do we solve the triangle one w/o using trig.... If its ont the SAT there should be a way to solve it without higher level math.</p>
<p>exactly, if its on the SAT, a 10th grader should be able to do it.</p>
<p>For the triangle question: </p>
<p>If you don't want to use trig, the only other option you have involves knowing the side ratios for a 30-60-90 right triangle. </p>
<p>Draw the altitude from P to MQ. The triangle's now been divided into two right triangles, one with angle measures 45-45-90, one with angle measures 30-60-90. </p>
<p>In any 30-60-90 triangle, the ratio of the sides (respectively) is 1-sqrt(3)-2. In other words, if the side across from the 30-degree angle is 1, the side across from the 60-degree angle is sqrt(3), and the hypotenuse has length 2. </p>
<p>Therefore, going back to the triangle in question: the 30-60-90 right triangle has hypotenuse 10. Applying the 30-60-90 ratio rule, the side across from the 30-degree angle (the altitude) has length 5, and the side across from the 60-degree angle has length 5sqrt(3). </p>
<p>Notice that the other right triangle has two 45-degree angles. It's isosceles, so the total length of MQ is equal to the sum of the lengths of the two legs of the 30-60-90 right triangle, or 5 + 5sqrt(3) = 13.66...</p>
<p>...I like my trig method better. XD The law of sines takes 5 minutes to memorize, tops, and is useful for questions like these to be found on the SAT.</p>
<p>Anyways, here is a picture of that triangle question the way I solved it.</p>
<p><a href="http://img.photobucket.com/albums/v413/jaimeastorga2000/Triangle-1.png%5B/url%5D">http://img.photobucket.com/albums/v413/jaimeastorga2000/Triangle-1.png</a></p>
<p>Now lemme tackle the first one.</p>
<p>First you graph the points and draw the lines connecting them. After doing that, the only logical place the fourth point can be is (3,3), so plot that. You should end up with this.</p>
<p><a href="http://img.photobucket.com/albums/v413/jaimeastorga2000/Square.png%5B/url%5D">http://img.photobucket.com/albums/v413/jaimeastorga2000/Square.png</a></p>
<p>After that, graph the equation y = -x, the line across which you will reflect the square. You should now have this.</p>
<p><a href="http://img.photobucket.com/albums/v413/jaimeastorga2000/SquareAndEquation.png%5B/url%5D">http://img.photobucket.com/albums/v413/jaimeastorga2000/SquareAndEquation.png</a></p>
<p>Finally, imagine folding the plane at the equation you have drawn. Or, if that's too theoretical for you, sketch the equation on the booklet and fold it across the line of the equation. Either way, you should see that it ends like this.</p>
<p><a href="http://img.photobucket.com/albums/v413/jaimeastorga2000/SquareAndEquationFlipped.png%5B/url%5D">http://img.photobucket.com/albums/v413/jaimeastorga2000/SquareAndEquationFlipped.png</a></p>
<p>The 3's indicate the lengths of the sides. Now that you have the four points, you simply have to check against your answers and see which one matches.</p>
