Question
Write down the equation of the line whose gradient is $\frac{3}{2}$and which passes through P. where P divides the line segment joining $A(−2, 6)$ and $B(3, −4)$ in the ratio $2 : 3$
✓
Answer
Given, P divides the line segment joining A $(−2, 6)$ and B $(3, −4)$ in the ratio $2: 3.$ Co-ordinates of point P are
$\left(\frac{2 \times 3+3 \times(-2)}{2+3}, \frac{2 \times(-4)+3 \times 6}{2+3}\right)$
$ =\frac{6-6}{5}, \frac{-8+18}{5}$
$=\frac{6-6}{5}, \frac{-8+18}{5}$
$ =(0.2)=\left(x_1, y_1\right)$
Slope of the required line $= m =\frac{3}{2}$
The required equation of the line is given by
$y − y_1 = m (x − x_1)$
$y-2=\frac{3}{2}(x-0)$
$2y − 4 = 3x$
$2y = 3x + 4$
$\left(\frac{2 \times 3+3 \times(-2)}{2+3}, \frac{2 \times(-4)+3 \times 6}{2+3}\right)$
$ =\frac{6-6}{5}, \frac{-8+18}{5}$
$=\frac{6-6}{5}, \frac{-8+18}{5}$
$ =(0.2)=\left(x_1, y_1\right)$
Slope of the required line $= m =\frac{3}{2}$
The required equation of the line is given by
$y − y_1 = m (x − x_1)$
$y-2=\frac{3}{2}(x-0)$
$2y − 4 = 3x$
$2y = 3x + 4$
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