Question

In the xy-plane, the line determined by the points (2,k) and (k,32) passes through the origin. Which of the following could be a value of k?

(A) 0
(B) 4
(C) 8
(D) 16

Answer 1

C

Explanation:

calculate the slope m of the 2 points from the origin and equate, since they lie on the same line

m =
`\frac{y_(2)-y_(1) }{x_{2-x_(1) } }`

with (x₁, y₁ ) = (0, 0 ) and (x₂, y₂ ) = (2, k )

m =
`(k-0)/(2-0)` =
`(k)/(2)`

repeat with

(x₁, y₁ ) = (0, 0 ) and (x₂, y₂ ) = k, 32 )

m =
`(32-0)/(k-0)` =
`(32)/(k)`

equating the 2 slopes

`(k)/(2)` =
`(32)/(k)` ( cross- multiply )

k² = 64 ( take square root of both sides )

k =
`√(64)` = 8