SOLUTION: True or false: the points (4,2) (8,10) and (11,16) are collinear

Question 1209384: True or false: the points (4,2) (8,10) and (11,16) are collinear
Found 3 solutions by mananth, math_tutor2020, greenestamps:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
Let the pointbes be A (4,2),B (8,10) and C (11,16)
If slope of AB = slope of BC then the points are co linear

If the points are (x1,y1) &(x2,y2) and (x3,y3)

(y3-y2)/(x3-x2) = (y2-y1)/(x2-x1)
(16-10)/(11-8) = 2
(10-2)/(8-4) =2
The points are co linear

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Label the points as A,B,C in any order you prefer.
A = (4,2)
B = (8,10)
C = (11,16)

Let's find the slope of line AB.
m = (y2 - y1)/(x2 - x1)
m = (10 - 2)/(8 - 4)
m = 8/4
m = 2

Do the same for line BC
m = (y2 - y1)/(x2 - x1)
m = (16 - 10)/(11 - 8)
m = 6/3
m = 2

Lines AB and BC have the same slope, so the three points are collinear.
Collinear points are on the same straight line.
You can use graphing tools like Desmos and GeoGebra to verify.
The equation of the line that goes through all three points is y = 2x-6

Answer: True

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The three points are collinear if the slope of the line containing (4,2) and (8,10) is the same as the slope of the line containing (8,10) and (11,16).

Of course you can use the formal formula for finding the slope of the line containing two points. But in my opinion it is more educational to use the informal "rise over run" definition of slope.

Between (4,2) and (8,10) the run is 8-4=4 and the rise is 10-2=8; the slope is rise/run = 8/4 = 2.

Between (8,10) and (11,16) the run is 16-10=6 and the rise is 11-8=3; the slope is rise/run = 6/3 = 2.

The slopes are the same, so the three points are collinear.

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