Can you solve this problem please

Question

asked Apr 8, 2022 18.5k views

2 Answers

Dougcunha · Answer 1 · 2022-04-14T11:21:06+0000

Answer:

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