A(5, 4), B(-3, -2) and C(1, -8) are the vertices of a triangle ABC. Find :

(i) the slope of the altitude of AB,

(ii) the slope of the median AD and

(iii) the slope of the line parallel to AC.

Plot the points A(1, 1), B(4, 7) and C(4, 10) on a graph paper. Connect A and B, and also A and C.

Which segment appears to have steeper slope, AB or AC?

Justify your conclusion by calculating the slopes of AB and AC.

Find the value(s) of k so that PQ will be parallel to RS. Given :

(i) P(2, 4), Q(3, 6), R(8, 1) and S(10, k)

(ii) P(3, -1), Q(7, 11), R(-1, -1) and S(1, k)

(iii) P(5, -1), Q(6, 11), R(6, -4k) and S(7, k²)