Question

Given the points (7,3) and (k,−7) , for which values of k would the distance between the points be 2√41? a. 14 or -4 b. 15 or -1 c. 17 or 2 d. 17 or -4

Answer 1

b

Explanation:

calculate the distance d between the 2 points and equate to 2
`√(41)`

calculate the distance using the distance formula

d =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = (7, 3 ) and (x₂, y₂ ) = (k, - 7 )

substitute these values into the formula for d

d =
`√((k-7)^2+(-7-3)^2)`

=
`√((k-7)^2+(-10)^2)`

=
`√((k-7)^2+100)`

now equate d to 2
`√(41)`

`√((k-7)^2+100)` = 2
`√(41)` ( square both sides to clear the radical )

(k - 7)² + 100 = ( 2
`√(41)` )² = 164 ( subtract 100 from both sides )

(k - 7)² = 64 ( take square root of both sides )

k - 7 = ±
`√(64)` = ± 8 ( add 7 to both sides )

k = 7 ± 8

Then values of k are

k = 7 + 8 = 15

k = 7 - 8 = - 1