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

Sagot :

Answer:

k = 3

Step-by-step 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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

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

m = [tex]\frac{16-4}{-3-1}[/tex] = [tex]\frac{12}{-4}[/tex] = - 3

Repeat with the point including k and equate to - 3

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

m = [tex]\frac{-2-16}{k-(-3)}[/tex] = [tex]\frac{-18}{k+3}[/tex] = - 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

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