Question

Write down the equation of the line whose gradian is \frac{2}{3} and which passes through P , where P divides the line segment joining A (-2, 6) \ and \ B (3, -4) in the ratio 2 : 3 [2001]​

Answer 1

Answer:

Step-by-step explanation:

P divides the line segment joining A (-2, 6) \and \B (3, -4) in the ratio 2 : 3

So the coordinates of P are

$P( \frac{2*3+3*-2}{2+3} ,\frac{2*-4+3*6}{2+3} \\\\\bf P (0,\frac{10}{5} ) \ or \ P(0,2)$

The gradient m=2/3

Let the equation is

y=2/3 x+c

This line passes through P(0,2)

Thus

2=0+c

c=2

Hence the equation is:

$y=\frac23 x +2\\\\3y=2x+6\\\\\bf Or \ 2x-3y+6=0$