Question

find the ratio in which the straight line 3x+4y=6 divides the line joining the points (2,-1)and (1,1)state whether the points lie on the same side or on the either side of the straight line​

Answer 1

Answer:

(x1,y1)=(2,-1)

(x2,y2)=(1,1)

x=x1+x2/2

x=2+1/3 = 3/2_________(1)

y=y1+y2=-1+1/2 = 0 ______(2)

putting the values of x and y in the given equation.

3x+4y=6

3(3/2)+4(0)=6

line is divided in the ratio of 7:2

Answer 2

Given : line 3x + 4y = 6

            Point A = (2, -1)

            Point B = (1, 1)

To find : Ratio of lines passing through point A and B

Solution :

Equation of the line is 3x + 4y = 6

Given points are A(2, −1) and B(1, 1).

The ratio in which the line L=0 divides the line join of point A and B is − $\frac{L_{11} }{L_{22} }$

= - $\frac{ax_{1} + by_{1} + c }{ax_{2} + by_{2} + c }$

= $\frac{(3 * 2) + (4 * (-1)) - 6}{(3 * 1) + (4 * 1) - 6}$

= $\frac{4}{1}$

The ratio is positive, therefore given points lie on opposite sides of the line.

#SPJ2

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