Question

The slope of a line joining P(6, k) and Q(1 – 3k, 3) is `1/2`. Find:

1. k.
2. mid-point of PQ, using the value of ‘k’ found in (i).

Answer 1

i. Slope of PQ = `(3 - k)/(1 - 3k - 6)`

`=> 1/2 = (3 - k)/(-3k - 5)`

`=>` –3k – 5 = 2(3 – k)

`=>` –3k – 5 = 6 – 2k

`=>` –3k + 2k = 6 + 5

`=>` –k = 11

`=>` k = –11

ii. Substituting k in P and Q, we get

P(6, k) = (6, –11)

And Q(1 – 3k, 3) = (1 – 3(–11), 3)

= (1 + 33, 3)

= (34, 3)

∴ Midpoint of PQ = `((6 + 34)/2, (-11 + 3)/2)`

= `(40/2, (-8)/2)`

= (20, −4)