Question

In the figure, line segment AB meets x - axis at A and y - axis at B. The point P(-3, 4) on AB divides it in the ratio 2 : 3. Find the coordinates of A and B.

[3 MARKS]

Answer 1

Formula: 1 Mark
Steps: 1 Mark
Answer: 1 Mark

A is (x, 0), B is (0, y), P is (-3, 4), $m_1:m_2=2:3$
For P:
$-3=\frac{m_1\left(0\right)+m_2\left(x\right)}{m_1+m_2}$
$\Rightarrow -3m_1-3m_2=m_{2}x$
$\Rightarrow -3\left(2\right)-3\left(3\right)=3\left(x\right)$
$\Rightarrow -15=3x\Rightarrow x=-5$
Also, $4=\frac{\left(2\right)\left(y\right)+\left(3\right)\left(0\right)}{2+3}$
$\Rightarrow 20=2y\Rightarrow y=10$
$\therefore$ Coordinates of A are (-5,0) and that of B are (0,10)