Question

Given a line segment AB joining the points A(-4, 6) and B(8, -3). Find:
(i) the ratio in which AB is divided by the y-axis
(ii) the coordinates of the point of intersection
(iii) the length of AB
[4 MARKS]

Answer 1

Part (i): 2 Marks
Part (ii): 1 Mark
part (iii): 1 Mark

i) On y-axis, x = 0
Let the $y-axis$ divide the line joining points A(-4, 6) and B(8, -3) in the ratio $m_1:m_2$
$\therefore 0=\frac{m_1\left(8\right)+m_2(-4)}{m_1+m_2}$
$\Rightarrow 8m_1=4m_2\Rightarrow m_1:m_2=1:2$

ii) $y=\frac{\left(1\right)(-3)+\left(2\right)\left(6\right)}{1+2}=\frac{-3+12}{3}=3$
$\therefore$ Point of intersection is (0,3)

iii) $AB=\sqrt{(-4-8{)}^2+(6+3{)}^2}$
$=\sqrt{144+81}=\sqrt{225}=15units$