(1)

(2) The line through (-3,9) and (4,4) has slope

The line through (9,-1) and (4,-8) has slope

Now

so the lines are perpendicular.

Note: We could have sketched the lines to determine whether they were parallel or perpendicular.

(3) This is the situation:

Applying the distance formula, we have:

Now so 5k² = 100, giving:

k² = 20

so

k = ± √20 ≈ ± 4.472

We obtained 2 solutions, so there are 2 possible outcomes, as follows: