Question

Plot the following points on the same graph paper and check whether they are collinear or not: 

(–1, –1), (2, 2) and (3, 3)

Answer 1

Given: Points A(–1, –1), B(2, 2) and C(3, 3).

Step-wise calculation:

1. Compute slope of AB:

`m_(AB) = (y_2 - y_1)/(x_2 - x_1)` 

= `(2 - (-1))/(2 - (-1))` 

= `3/3` 

= 1

2. Compute slope of BC:

`m_(BC) = (3 - 2)/(3 - 2)` 

= `1/1` 

= 1

3. Compute slope of AC:

`m_(AC) = (3 - (-1))/(3 - (-1))` 

= `4/4` 

= 1

4. All three slopes are equal (m_AB = m_BC = m_AC = 1), so the points lie on the same straight line.

Also note: each point satisfies y = x, since –1 = –1, 2 = 2, 3 = 3, so they all lie on the line y = x.

The points (–1, –1), (2, 2) and (3, 3) are collinear; they lie on the line y = x.