Question

The slope of a line joining P(6, k) and Q(1-3k, 3) is $\frac{1}{2}$. Find :

(i) k.

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

Answer 1

(i) ∴ m = (3 - k)/(1 - 3k - 6)
= (3 - k)/(- 5 - 3k)

∴ (3 - k)/(- 5 - 3k) = 1/2
∴ 2 (3 - k) = 1 (- 5 - 3k)
∴ 6 - 2k = - 5 - 3k
∴ k = - 11

(ii) We now have P = (6, -11) and Q = (34,3)

Use mid - point formula:
∴ M = ((x1 + x2)/2, (y1 + y2)/2)
= ((6+34)/2, (-11+3)/2)
= (20, - 4)

Thus, the mid - point of PQ is (20, - 4).