(a) Find the points which divide the line joining A(1,3) and B(-4,-1) internally in the ratios:

(i) 1:2

(ii) 1:1

(iii) 3:1

(b) On the same x-y axes plot the point A(1,3) and B(-4,-1) and draw the line joining them. Add the three points which you calculated in part (a).

2 answers

(1,3), (x,y), (-4,-1).

(i). -4-x = 2(x-1).
-4-x = 2x-2, X = -2/3.

-1-y = 2(y-3).
-1-y = 2y-6, Y = 5/3.

(ii). x-1 = -4-x.
X = -3/2.

y-3 = -1-y. Y = 1.
(iii). x-1 = 3(-4-x).
x-1 = -12-3x, X = -11/4.

y-3 = 3(-1-y).
y-3 = -3-3y, Y = 0.