Answer:
C
Step-by-step explanation:
calculate the slope m of the 2 points from the origin and equate, since they lie on the same line
m = [tex]\frac{y_{2}-y_{1} }{x_{2-x_{1} } }[/tex]
with (x₁, y₁ ) = (0, 0 ) and (x₂, y₂ ) = (2, k )
m = [tex]\frac{k-0}{2-0}[/tex] = [tex]\frac{k}{2}[/tex]
repeat with
(x₁, y₁ ) = (0, 0 ) and (x₂, y₂ ) = k, 32 )
m = [tex]\frac{32-0}{k-0}[/tex] = [tex]\frac{32}{k}[/tex]
equating the 2 slopes
[tex]\frac{k}{2}[/tex] = [tex]\frac{32}{k}[/tex] ( cross- multiply )
k² = 64 ( take square root of both sides )
k = [tex]\sqrt{64}[/tex] = 8
