Question

find the value of x for the points (x,-1) (2,1) and (4,5) are collinear

Answer 1

Answer:

x = 1

Step-by-step explanation:

If the points are collinear, it means that their gradients are the same.

Find the gradient of (x, -1) and (2, 1)

Gradient = (y2 - y1) / (x2 - x1)

Gradient = (1 - (-1) ) / (2 - x) = 2/(2 - x)

Find the gradient of (2, 1) and (4, 5)

Gradient = (y2 - y1) / (x2 - x1)

Gradient = (5 - 1)/(4 - 2) = 4/2 = 2

Since the gradients are the same:

2/(2 - x) = 2

2 = 2(2 - x)

2 = 4 - 2x

2x = 2

x = 1

Answer: x = 1