Question

Can you solve this problem please​

Answer 1

Answer: K=11

Step-by-step explanation:

Answer 2

k = 11

Step-by-step explanation:

Given the points are collinear then the slopes between consecutive points are equal.

Using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (1, - 1)

m =
`(-1-1)/(1-5)` =
`(-2)/(-4)` =
`(1)/(2)`

Repeat with another 2 points and equate to
`(1)/(2)`

with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (k, 4)

m =
`(4+1)/(k-1)` , then

`(5)/(k-1)` =
`(1)/(2)` ( cross- multiply )

k - 1 = 10 ( add 1 to both sides )

k = 11