Question

Find the ratio in which the line segment joining A( 1,-5 ) and B ( -4,5) is divided by the x- axis. Also

find the coordinates of the point of division​

Answer 1

(refer to the attachment)

★GIVEN★

• Coordinate of A(1,-5) = x.
• Coordinate of B(-4,5) = y.
• The line is divided by x-axis.

★To Find★

• The ratio in which the line segment joining.
• The coordinates of the point of division.

★SOLUTION★

Coordinate of point P is (x,0) because the line is divided by x-axis.

Let the ratio (m : n) be (k : 1).

• m = k and n = 1.
• $\large{\sf{Let\:x_{1}\:and\:x_{2}\:be\:1,-4\:respectively.}}$
• $\large{\sf{Let\:y_{1}\:and\:y_{2}\:be\:-5,5\:respectively.}}$

We know that,

$\large{\orange{\underline{\boxed{\bf{For\:x=\dfrac{mx_{2}+nx_{1}}{m+n}}}}}}$

$\large{\orange{\underline{\boxed{\bf{For\:y=\dfrac{my_{2}+ny_{1}}{m+n}}}}}}$

Now,

Coordinate of P is (0,x).

Putting the values,

For x,

$\large\implies{\sf{\dfrac{mx_{2}+nx_{1}}{m+n}}}$

$\large\implies{\sf{\dfrac{k\times(-4)+1\times1}{k+1}}}$

$\large\implies{\sf{\dfrac{-4k+1}{k+1}\quad\:{\bf\orange{eq.(i)}}}}$

For y,

$\large\implies{\sf{\dfrac{my_{2}+ny_{1}}{m+n}}}$

$\large\implies{\sf{\dfrac{k\times5+1\times(-5)}{k+1}}}$

$\large\implies{\sf{\dfrac{5k+(-5)}{k+1}}}$

$\large\implies{\sf{\dfrac{5k-5}{k+1}\quad\:{\bf\orange{eq.(ii)}}}}$

Now according to the question,

$\large\implies{\sf{\dfrac{5k-5}{k+1}=0}}$

$\large\implies{\sf{5k-5=0\times\:(k+1)}}$

$\large\implies{\sf{5k-5=0}}$

$\large\implies{\sf{5k=5}}$

$\large\implies{\sf{k=\dfrac{5}{5}}}$

$\large\implies{\sf{k=\dfrac{\cancel{5}}{\cancel{5}}}}$

$\large\therefore\boxed{\bf{k=1}}$

So by putting the value of k = 1 in eq.(i),

$\large\implies{\sf{\dfrac{-4k+1}{k+1}=x}}$

$\large\implies{\sf{\dfrac{(-4)\times1+1}{1+1}=x}}$

$\large\implies{\sf{\dfrac{(-4)+1}{2}=x}}$

$\large\implies{\sf{\dfrac{-4+1}{2}=x}}$

$\large\implies{\sf{-3=2x}}$

$\large\implies{\sf{\dfrac{-3}{2}=x}}$

$\large\therefore\boxed{\bf{x=\dfrac{-3}{2}}}$

$\large{\orange{\underline{\boxed{\therefore{\bf{Coordinate\:of\:P(\dfrac{-3}{2},0).}}}}}}$

$\large{\orange{\underline{\boxed{\therefore{\bf{The\:Ratio\:is\:(1:1).}}}}}}$

Answer 2

Answer:

hii epdii irukaa... ☺☺☺