Question

If the coordinates of A and B respectively are (-4, 3) and (8, -6), then
(i) find the length of AB.
(ii) In what ratio, is the line joining AB divided by the x-axis?
[4 MARKS]

Answer 1

Part (i): 1 Mark
Part (ii): 3 Marks

(i) The coordinates of A and B are (-4, 3 ) and (8, -6) respectively.
$|AB|=\sqrt{(8+4{)}^2+(-6-3{)}^2}=\sqrt{144+81}=\sqrt{225}|AB|=15units$

(ii) Let x-axis divides the line AB in the ratio k:1
Using section formula, we have
$\Rightarrow 0=\frac{-6k+3}{k+1}\Rightarrow k=\frac{1}{2}$
The line joining AB is divided by the x-axis in the ratio 1 : 2