SOLUTION: do the points in the following set lie on the same line? explain your answer show all your work. A(1,3) B(4,2) C(-2,4)

Algebra ->  Length-and-distance -> SOLUTION: do the points in the following set lie on the same line? explain your answer show all your work. A(1,3) B(4,2) C(-2,4)      Log On


   

Question 1139366: do the points in the following set lie on the same line? explain your answer show all your work. A(1,3) B(4,2) C(-2,4)
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
m=%282-3%29%2F%284-1%29=-1%2F3
y-3=-%281%2F3%29%28x-1%29
y=-%281%2F3%29%28x-1%29%2B3
y=-x%2F3%2B1%2F3%2B3
y=-x%2F3%2B3%261%2F3-----------line AB

true or false: 4=-%281%2F3%29%2A%28-2%29%2B3%261%2F3
OR
Is point C on line AB?
-
4=2%2F3%2B3%261%2F3
TRUE

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


There are many formal mathematical methods for finding the answer. One of them is what the other tutor did; find the equation determined by two of the points and see if the third point satisfies that equation.

That's mathematically valid; but not very efficient.

I would find the answer by comparing the slopes between pairs of points.

And I would find the answer by using my UNDERSTANDING of slopes, rather than using the formal mathematical definition of slope.

Picture the three given points; from left to right, the points are C, A, B. Determine how far you move to the right, and how far you move up or down, to get from C to A. Then do the same from A to B.

C(-2,4) to A(1,3): right 3, down 1.

A(1,3) to B(4,2): right 3, down 1.

If you have a basic understanding of slope, those results tell you that the slope from C to A is the same as the slope from A to B; therefore the three points lie on the same line.