<p>This is from the 2010 Wednesday PSAT.</p>
<ol>
<li>In the xy-plane, the two points A (-2,-5) and B (3,2) are each reflected about the line y=x. What is the slope of the line containing the points to which A and B are reflected?</li>
</ol>
<p>A. -7/5</p>
<p>B. -5/7</p>
<p>C. 1/7</p>
<p>D. 5/7</p>
<p>E. 7/5</p>
<p>The answer is D, and I cannot figure out why for the life of me.</p>
<p>a reflection over the y=x line is the inverse. Just switch the x and y coordinates and find the new slope (e.g. use (-5,-2)and(2,3)</p>
<p>^Beat me to it. In general, **a reflection over the line y=x means:</p>
<p>(X,Y) -> (Y, X).**</p>
<p>In this case:</p>
<p>(3,2) -> (2, 3)
(-2,-5) -> (-5,-2)</p>
<p>Slope:</p>
<p>-2-3 = -5 (change in y)</p>
<p>-5-2 = -7 (change in x) </p>
<p>-5/-7 = 5/7 = Answer Choice D.</p>
<p>Problem from the recent PSAT I suppose?</p>
<p>^Yes. 10char.</p>
<p>
</p>
<p>Dusterbug,</p>
<p>IceQube nailed the answer dead on. First you want to (if need be) just sketch the points and the line y=x. Then realize the translation formula switches the (x,y) coordinates. Finally, the slope formula is Delta y/delta x, meaning (y2-y1)/(x2-x1).</p>
<p>~Aceventura74</p>
<p>All right thanks everybody, I knew there was something specific I was supposed to be doing to solve this. I don’t think I ever actually learned that reflections invert the x,y coordinates. glad I learned that now</p>
<p>Dusterbug,</p>
<p>If you can’t remember an exact translation formula, you can always sketch it out. Physically draw it on a scrap grid and think about a reflection. That always helped me before I learned my rules. </p>
<p>~Aceventura74</p>
<p>Dusterbug,</p>
<p>Reflections in general don’t interchange the x and y values. The SPECIFIC reflection in the line y=x does this.</p>
<p>A reflection in the y-axis negates the x-coordinate.
A reflection in the x-axis negates the y-coordinate.</p>
<p>Although it’s worth memorizing these, keep in mind that if you forget you can just draw a picture.</p>