SOLUTION: A(-1,2), B (3,a) and C (-3,7) are collinear. Find a

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Question 976427: A(-1,2), B (3,a) and C (-3,7) are collinear. Find a
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's find the equation of the line through the two points (-1,2) and (-3,7)


To do that, we use the slope formula to find the slope m.

Note: is the first point . So this means that x%5B1%5D=-1 and y%5B1%5D=2.
Also, is the second point . So this means that x%5B2%5D=-3 and y%5B2%5D=7.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%287-2%29%2F%28-3--1%29 Plug in y%5B2%5D=7, y%5B1%5D=2, x%5B2%5D=-3, and x%5B1%5D=-1


m=%285%29%2F%28-3--1%29 Subtract 2 from 7 to get 5


m=%285%29%2F%28-2%29 Subtract -1 from -3 to get -2


m=-5%2F2 Reduce


So the slope of the line that goes through the points and is m=-5%2F2


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-2=%28-5%2F2%29%28x--1%29 Plug in m=-5%2F2, x%5B1%5D=-1, and y%5B1%5D=2


y-2=%28-5%2F2%29%28x%2B1%29 Rewrite x--1 as x%2B1


y-2=%28-5%2F2%29x%2B%28-5%2F2%29%281%29 Distribute


y-2=%28-5%2F2%29x-5%2F2 Multiply


y=%28-5%2F2%29x-5%2F2%2B2 Add 2 to both sides.


y=%28-5%2F2%29x-1%2F2 Combine like terms.


So the equation that goes through the points and is y=%28-5%2F2%29x-1%2F2

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Now plug in x = 3 to find y

y=%28-5%2F2%29x-1%2F2

y=%28-5%2F2%29%283%29-1%2F2

y=-15%2F2-1%2F2

y=%28-15-1%29%2F2

y=-16%2F2

y=-8

So the point (3,-8) lies on the same line. Therefore, a = -8
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