An easy 10 points right here?

Question

The problem asks to find the distance between the points:

(2k, 4k), (3k, 6k)

So I did:

D = square root of (k² + (2k)²)

...= square root of (5k²)

...= square root of (5) * k

...= k * square root of (5)

But the answer says its |k|squareroot(5).

Does it have to do with when

square root of (5k²) has squareroot(k²) therefore k must be a positive number?

but then why can't the person first square the k, then take the square root?

Thank you all in advance.

Answer 1

distances can't be negative......simple as that

even if k is negative, there will be a positive distance between the two points

Answer 2

D = √(2k-3k)² + (4k-6k)²

   = √k² + 4k²

   = √5k² = √5 x √k²

   = k√5

Answer 3

Yes its right. We do not know if k<0 or k>0. But we do know the distance ca never be negative. So |k| rt5 is correct.

Say of the points are in Quad 3 the k<0 but distance is ia not<0

Answer 4

Suppose k is -2

Then the distance between (-4, -8) and (-6, -12)

is the same as the diatance between (4, 8) and (6, 12) when k is +2.

And since distance is always positive, the answer is |k| sqrt(5)

  

Answer 5

there are 2 cases

k is positive or zero in which case case k *sqrt(5) is correct

but k could be -ve. this case the points are in 3rd quadrant and

k * sqrt(5) is -ve and so we need to take |k| sqrt(5)

|k| sqrt(5) is positive and correct for all k

so |k| sqrt(5) is correct ans

Answer 6

actually...the answer can be improved to |k√5| because it could be |k|(±√5) if it took the value |k|(-√5), the answer would not be accepted.

other than this, the reasons provided by other members ie distance cant be negative in value, would suffice (: