Question

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

1) k

2) A midpoint of PQ, using the value of ‘k’ found in (1).

Answer 1

1) Slope of PQ = `(3-k)/(1 - 3k - 6)`

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

⇒ -3k - 5 = 2(3 - k)

⇒ -3k - 5 = 6 - 2k

=> k = -11

2) Substituting k in P and Q, we get

P(6, k) = P 6, 11 and Q(1-3k,3) = Q(34,3)

∴ Midpoint of PQ = `((6+34)/2 , (-11+3)/2) = (40/2 , (-8)/2) = (20 , -4)`