<p>Guys, I got this question right but, it took me a couple of minutes so I was wondering if i got it the long way so, I wanted to know if there's a short way, The question is</p>
<p>in the xy-coordinate plane, lines L and Q are perpendicular, If line L contains the points (0,0) and (2,1), and line Q contains the points (2,1) and (0,t), what is the value of t ?
The answer is 5</p>
<p>the answer would be 5.</p>
<p>simple. perpendicular has to be negative reciprocal.</p>
<p>1-0/2-0 is 1/2 right?</p>
<p>then perpen needs to be -2</p>
<p>so 5-1/0-2 = -2</p>
<p>I took about half a minute doing it this way.
Slope of line L = delta y/ delta x = 1/2
perpendicular slope of L = negative reciprocal = -2
Slope of line G = delta y/ delta x = -2
(t-1)/(0-2) = -2, solve for t, t =5</p>
<p>Q and L are perpendicular, so their slopes are negative reciprocals or the product of their slopes is negative 1. So
ML=1/2 and MQ=(t-1)/(-2)
1/2 times (t-1)/(-2)=-1===>t-1=4 ==>t=5</p>
<p>I always start these problems with a neat diagram, hoping it will get me out of doing any actual math. If you draw a neat x-y axis and then mark (0,0) and (2,1)…then start from (2,1) – you know you have to get back to the y-axis, and to be perpendicular, you have to go back 1, up 2, back 1, up 2…you land on (0,5).</p>
<p>What I just wrote will not make any sense unless you draw the picture. But if you do, you’ll see what i meant.</p>