Exercise 51 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 for G and H, H and I, and G and I using the Slope Formula. Let's start with G and H.

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

SubstitutePoints

Substitute ( 3,5) & ( -1,3)

m_(GH)=3- 5/-1- 3

SubTerms

Subtract terms

m_(GH)=-2/-4

DivNegNeg

- a/- b=a/b

m_(GH)=2/4

ReduceFrac

a/b=.a /2./.b /2.

m_(GH)=1/2

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	Slope
G (3,5), H (- 1,3)	3- 5/- 1- 3	1/2
H (-1,3), I (7,7)	7- 3/7-( -1)	1/2
G (3,5), I (7,7)	7- 5/7- 3	1/2

Notice that all pairs of points have a slope of 12. Thus, all points in the given set lie on the same line.