Question
Write down the equation of the line whose gradient is $-2/5$ and which passes through point $P,$ where $P$ divides the line segement joining $A(4, −8)$ and $B (12, 0)$ in the ratio $3 : 1$
✓
Answer
Given, $P$ divides the line segment joining $A (4, -8)$ and $B (12, 0)$ in the ratio $3: 1.$ Co-ordinates of point $P$ are
$\left(\frac{3 \times 12+1 \times 4}{3+1}, \frac{3 \times 0+1 \times(-8)}{3+1}\right)$
$=\left(\frac{36+4}{4}, \frac{-8}{4}\right)$
$=(10,-2)$
slope $=m=-\frac{2}{5}$ (given)
Thus, the required equation of the line is
$y − y_1 = m (x − x_1)$
$y + 2 =(-2)/5(x − 10)$
$5y + 10 = -2x + 20$
$2x + 5y = 10$
$\left(\frac{3 \times 12+1 \times 4}{3+1}, \frac{3 \times 0+1 \times(-8)}{3+1}\right)$
$=\left(\frac{36+4}{4}, \frac{-8}{4}\right)$
$=(10,-2)$
slope $=m=-\frac{2}{5}$ (given)
Thus, the required equation of the line is
$y − y_1 = m (x − x_1)$
$y + 2 =(-2)/5(x − 10)$
$5y + 10 = -2x + 20$
$2x + 5y = 10$
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