Question

the ratio in which the line segment joining the points 1, 0 and -1, 0 divided by 0, 0​

Answer 1

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Answer 2

Point (0,0) divide (1,0) and (-1,0) in ratio 1:1

Step-by-step explanation:

1. Let point (1,0) be represented by A,So

   $\mathbf{A(x_{1},y_{1})=(1,0)}$

2. Let point (-1,0) be represented by B,So

   $\mathbf{B(x_{2},y_{2})=(-1,0)}$

3. Let point (0,0) be represented by C,So

   $\mathbf{C(x,y)=(0,0)}$

4. Let point C divide A and B in m:1

5. Point C can be written as

   

   $\mathbf{(x,y)=\left ( \frac{m\times x_{2}+1\times x_{1}}{m+1},\frac{m\times y_{2}+1\times y_{1}}{m+1} \right )}$        ...1)

6. Now putting respective value in equation 1), we get

  $\mathbf{(0,0)=\left ( \frac{m\times (-1)+1\times 1}{m+1},\frac{m\times 0+1\times 0}{m+1} \right )}$

  $\mathbf{(0,0)=\left ( \frac{-m+1}{m+1},\frac{0}{m+1} \right )}$       ...2)

7. Now comparing the corresponding term in equation 2), we get

   $\mathbf{0=\frac{-m+1}{m+1}}$

   So

   -m+1=0

   means

   m=1

8. Point C divide A and B in m:1, which means point C divide A and B in      1:1