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all lie on the same line

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all lie on the same line

by sanju09 » Wed Sep 15, 2010 9:50 pm
If points (0, -3), (6, 0) and (k, 10) all lie on the same line, what is the value of k?
(A) 2
(B) 8
(C) 14
(D) 22
(E) 26


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by Neo Gates » Thu Sep 16, 2010 2:55 am
sanju09 wrote:If points (0, -3), (6, 0) and (k, 10) all lie on the same line, what is the value of k?
(A) 2
(B) 8
(C) 14
(D) 22
(E) 26


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by MariaS » Thu Sep 16, 2010 4:23 am
Let's draw the points and the line:


Image

Point (k,10) is show in yellow on line y=10 (the purple line). In order to find value k, we need to find the the line that connects all 3 points (shown in orange).
We can find it with the 2 points we are given: (6,0) and (0,-3). the slope is worth: (Change in Y)/Change in x) = [0-(-3)] / (6-0) =3/6=1/2
so the equation of the line we are looking for is: y-y'=slope(x-x') where slope is 1/2, as shown above, and (x',y') are the coordinates of any point residing on this line. We are given 2 of points, so use of either one will do: y-(-3)=(1/2)*(x-0) --> y=(1/2)x-3.
We are given that point (k, 10) is also on this line, so: (1/2)k-3=10 --> (1/2)k=13 --> k=26
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