Question

For what value of k will make the three points (1,4),(-3,16)and(k,-2)collinear?​

Answer 1

k = 3

Explanation:

Collinear means the points lie on the same line , thus the slope between consecutive points is equal.

Calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (1, 4 ) and (x₂, y₂ ) = (- 3, 16 )

m =
`(16-4)/(-3-1)` =
`(12)/(-4)` = - 3

Repeat with the point including k and equate to - 3

(x₁, y₁ ) = (- 3, 16 ) and (x₂, y₂ ) = (k, - 2 )

m =
`(-2-16)/(k-(-3))` =
`(-18)/(k+3)` = - 3 ( multiply both sides by k + 3 )

- 18 = - 3(k + 3) ← divide both sides by - 3

6 = k + 3 ( subtract 3 from both sides )

3 = k