Question

The points 1 , B and ( are (9 , 8) , ( 12, 4) and (4, - 2) respectively

(a) Find
(1)
the gradient of the line through d and B
(¡i)
the equation of the line through C which is parallel to AB
(b) Calculate the length of the line segment
(i)
[21
(11)
BC
[21
(c) Show that AB is perpendicular to BC 121
(d) Calculate the area of triangle ABC
[1)

Answer 1

a.i.

`mab = (ya - yb)/( xa - xb) = (8 - 4)/(9 - 12) = (4)/( -3)`

a.ii.

`mc = mab = (4)/( - 3) \\ (y - y1) = m(x - x1) \\ y - ( - 2) = (4)/( - 3)(x - 4) \\ y + 2 = (4)/( - 3)x + (16)/(3) \\ y = (4)/( - 3) x + (16)/( 3) - 2 \\ y = (4)/( - 3)x + (10)/(3)`