Question

20. Find the equation of the line whose gradient is 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 internally

Answer 1

Final Answer : y=23x+2

Steps:
1) Slope of line,m = 23
Since, P divides A (-2,3) and B(3,-4) in the ratio
2:3 internally.

By Section Formula,
P(x,y) =
$x = \frac{(3 \times - 2 + 2 \times 3)}{2 + 3} \: \: \: \: \: \: \: y = \frac{(2 \times - 4 + 3 \times 6)}{2 + 3} \\ = > x = \frac{0}{5} \: \: \: y = \frac{10}{5} \\ = > x = 0 \\ = > y = 2$

3) Slope of line : m = 23
Point on line, P(x,y) = (0,2)
Now,
Equation of line :
Slope Form :
(y-2)=23(x-0)
=> y = 23x + 2

Answer 2

Solution:-

given by:-


we have:-

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

》Slope of the line = 3/2

 》= (L x₂ + m x₁)/(L + m) , (L y₂ + m y₁)/(L + m)

》  = [2(3) + 3 (-2)]/(2 + 3) , [2(-4) + 3 (6)]/(2 + 3)

》  = [6 - 6]/5 , [-8 + 18]/5

》      = 0/5 , 10/5

》       = (0 , 2)

Equation of the line:
by formula:-


》(y - y₁) = m (x - x₁)

》(y - 2) = (3/2) (x - 0)

》2(y - 2) = 3 x

》2y - 4 = 3x

》3x - 2y + 4 = 0

equation of the line ( 3x-2y+4=0) ans

☆i hope its help☆