Question
Points $A, B, C$ and $D$ divide the line segment joining the point $(5, -10)$ and the origin in five equal parts. Find the co-ordinates of $B$ and $D.$
✓
Answer
Point $A$ divides $PO$ in the ratio $1: 4.$
Co-ordinates of point A are:
$\left(\frac{1 \times 0+4 \times 5}{1+4}, \frac{1 \times 0+4 \times(-10)}{1+4}\right)$
$=\left(\frac{20}{5},-\frac{40}{5}\right)$
$=(4,-8)$
Point $B$ divides $PO$ in the ratio $2: 3.$
Co-ordinates of point $B$ are:
$\left(\frac{2 \times 0+3 \times 5}{2+3}, \frac{2 \times 0+3 \times(-10)}{2+3}\right)$
$=\left(\frac{15}{5},-\frac{30}{5}\right)$
$=(3,-6)$
Point $C$ divides $PO$ in the ratio $3: 2.$
Co-ordinates of point $C$ are:
$\left(\frac{3 \times 0+2 \times 5}{3+2}, \frac{3 \times 0+2 \times(-10)}{3+2}\right)$
$=\left(\frac{10}{5},-\frac{20}{5}\right)$
$=(2,-4)$
Point $D$ divides $PO$ in the ratio $4: 1.$
Co-ordinates of point $D$ are:
$\left(\frac{4 \times 0+1 \times 5}{4+1}, \frac{4 \times 0+1 \times(-10)}{4+1}\right)$
$=\left(\frac{5}{5},-\frac{10}{5}\right)$
$=(1,-2)$
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