Slope Of A Line

For three points to be collinear, the slopes between any two points must be equal. The slope between points

(5%2C%205)

and

(-5%2C%201)

is:

%5Ctext%7Bslope%7D%20%3D%20%5Cfrac%7B1%20-%205%7D%7B-5%20-%205%7D%20%3D%20%5Cfrac%7B-4%7D%7B-10%7D%20%3D%20%5Cfrac%7B2%7D%7B5%7D

The slope between points

(5%2C%205)

and

(10%2C%20k)

is:

%5Ctext%7Bslope%7D%20%3D%20%5Cfrac%7Bk%20-%205%7D%7B10%20-%205%7D%20%3D%20%5Cfrac%7Bk%20-%205%7D%7B5%7D

Since the points are collinear, these two slopes must be equal:

%5Cfrac%7Bk%20-%205%7D%7B5%7D%20%3D%20%5Cfrac%7B2%7D%7B5%7D

Multiplying both sides by 5:

k%20-%205%20%3D%202%20%5Cquad%20%5CRightarrow%20%5Cquad%20k%20%3D%207

Therefore, the correct answer is

k%20%3D%207

Chapter Questions
1 MCQs