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)

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) (Show Source): You can put this solution on YOUR website!

-----------line AB

true or false:
OR
Is point C on line AB?
-

TRUE
Answer by greenestamps(13203) (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.
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