Please help me? 10 easy points?

Question

Find the value of K if the line joining (4,K) and (6,8) and the line joining (-1,4) and (0,8) are (a)parallel, (b) perpendicular.

Please help me, I don't even understand the question itself.

Answer 1

Line joining the 2 points:

y2 - y1

----------

x2 - x1

8-4

----------

0- -1

4/1= 4

a) parallel lines have the same slope

(8-k) / (6-4) = 4/1

(8-k) / 2 = 4/1

8-k = 8

-k = 0

k = 0

b) perpendicular lines have opposite reciprocal slopes

(8-k) / (6-4) = -1/4

(8-k) / 2 = -1/4

4(8-k) = -2

32 - 4k = -2

-4k = -34

k = 34/4

k = 17/2