Question

(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).

Answer 1

I will do the first one, you do the other two in the same way.
Let P(x, y) be on AB so that
AP/PB = 1/2

for the x:
(x-1)/(-4-x) = 1/2
2x - 2 = -4 - x
3x = -2
x = -2/3

for the y:
(y-3)/(-1-y) = 1/2
2y - 6 = -1 - y
3y = 5
y = 5/3
so P is (-2/3 , 5/3)

for b), I am sure you meant "plot" the three points.
We cannot "add" points in this context.