Given:
Three points are:
A(x, −1), B(2, 1) and C(4, 5)
For three points to be collinear, the slopes of any two pairs must be equal.
Step 1: Find slope of BC
Slope of BC =
(5 − 1) / (4 − 2)
= 4 / 2
= 2
Step 2: Find slope of AB
Slope of AB =
(1 − (−1)) / (2 − x)
= 2 / (2 − x)
Step 3: Equate the slopes
Since the points are collinear:
Slope AB = Slope BC
2 / (2 − x) = 2
Step 4: Solve for x
2 = 2(2 − x)
1 = 2 − x
x = 1
Final Answer:
The value of x for which the points are collinear is
x = 1