Exercise 54 Page 300

Points that lie on the same line are called collinear points. If the given points are collinear, the slope between every pair of points will be equal. To determine the slope between each pair of points, we will use the Slope Formula. m = y_2-y_1/x_2-x_1We will calculate the slope between G and H, H and I, and G and I. Let's start with G and H.

m_(GH)=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 1,- 2) & ( - 1,- 5)

m_(GH)=- 5-( - 2)/- 1- 1

SubNeg

a-(- b)=a+b

m_(GH)=- 5+2/- 1-1

AddSubTerms

Add and subtract terms

m_(GH)=- 3/- 2

DivNegNeg

- a/- b=a/b

m_(GH)=3/2

We can calculate the other two slopes in the same way. When we substitute the values into the Slope Formula, it does not matter which point we choose to use as (x_1,y_1) or (x_2,y_2).

Points	y_2-y_1/x_2-x_1	m
G (1,- 2), H (- 1,- 5)	- 5-( - 2)/- 1- 1	3/2
H (- 1,- 5), I (5,4)	4-( - 5)/5-( - 1)	3/2
G (1,- 2), I (5,4)	4-( - 2)/5- 1	3/2

Notice that all pairs of points have a slope of 32. Thus, all the points in the given set lie on the same line.