Question

The interval with end points P(–4, 5) and Q(6, 1) is bisected by the straight line n. Therefore the midpoint of PQ lies on n and satisfies its equation.

Which of the following could be the equation of line n? Write in general formula and show all working

Answer 1

m = (1 - 5)/(6 - (-4)) = -4/10 = -2/5

5 = (-2/5)(-4) + b

5 = 8/5 + b

b = 17/5

y = (-2/5)x + 17/5

Assume that line n is perpendicular to PQ. Line n will have slope 5/2.

The midpoint of PQ is ((-4 + 6)/2, (5 + 1)/2) = (1, 3).

3 = (5/2)(1) + b

3 = 5/2 + b

b = 1/2

y = (5/2)x + (1/2) could be the equation of line n.