Question

Use the concept of slope to determine whether the three points are collinear.

(0, 2), (8, −8), (−3, 10)

The three points are collinear. The three points are not collinear.

Answer 1

If the points are co-linear, the slopes between the first and second and second and third will be the same.

(-8-2)/(8-0) and (10-(-8))/(-3-8). That is, -10/8=-5/4 and 18/-11=-18/11. These two slopes are not the same, so the points are not co-linear.

 

Answer 2

Given (x_1,y_1)=(0,2)
(x_2,y_2)=(8,-8)
(x_3,y_3)=(-3,10)

Distance between two points (x_1,y_1)=(0,2)
(x_2,y_2)=(8,-8)

d=√((-8-2)^2+(8-0)^2)
d=2√14

Distance between two points (x_2,y_2)=(8,-8)
(x_3,y_3)=(-3,10)
d=√((10+8)^2+(-3+8)^2)
d=√349

Distance between two points (x_1,y_1)=(0,2)
(x_3,y_3)=(-3,10)
d=√((10-2)^2+(-3-0)^2)
d=√73

2√14+√349=√73

Hence The three points are not collinear.

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