help on math question ! (not from BB)

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1

<p>So, at first glance, the question looks pretty easy. I cant get the answer though.</p>

<p>"In the xy-plane, a line contains the points (4,2), (-2, -1) and (k, 5)</p>

2

<p>ops, it went wrong. just a sec</p>

<p>So, at first glance, the question looks pretty easy. I cant get the answer though.</p>

<p>“In the xy-plane, a line contains the points (4,2), (-2, -1) and (k, 5). How do you find k ?”</p>

<p>there you go</p>

3

<p>I first tried to find the slope (1/3 i think) and then i tried to put (4, 2) in the equation (y=mx+b) to find b (2/3), and finally i tried to put (x, 5) on the equation, but it doesn’t work ! I cant find the same result (8) that i do when i draw a graph.</p>

4

<p>A cheap but valid solution is to look at the y-coordinates – 2 is the midpoint of -1 and 5, so because the three points are on a line, 4 must be the midpoint of -2 and k, so k = 10.</p>

<p>You can also find the equation of the line containing (4,2) and (-2,-1) (which turns out to be y = x/2). Then 5 = k/2 --> k = 10.</p>

5

<p>well though ! but how do you know the equation is y=x/2 ?</p>

<p>edit: OH, i got it now ! thank for the help :)</p>

6

<p>The slope of the line connecting (4,2) and (-2,-1) is 1/2. Therefore the equation is of the form y = (1/2)x + b where b is a constant. But substituting (4,2) or (-2,-1) gives b = 0, so y = x/2.</p>

7

<p>You know the slope between any two collinear points must be the same. So find the slope for the first two points:</p>

<p>(2 - -1)/(4 - -2) = 3/6 = 1/2</p>

<p>You know the slope between (4,2) and (k,5) must also be 1/2, so</p>

<p>(5-2)/(k-4) = 1/2</p>

<p>3/(k-4) = 1/2</p>

<p>k - 4 = 6</p>

<p>k = 10</p>

8

<p>MITers solution is best here. When given points on a line with one missing coordinate in any form (this could be points, a table, values of a linear function, a graph), just remember that equal “x-jumps” give the same “y-jumps.” This way you can get the answer in just a few seconds by counting. </p>

<p>(I wouldn’t call that a cheap solution - I would say it should be the standard way to solve this type of problem).</p>