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If one end of the line segment is (1, 2) and the point which divides internally in the ratio 1 : 2 is origin, find the other externally.

plane-geometry

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asked Aug 3 at 5:54

user581382

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put on hold as off-topic by Henrik, Claude Leibovici, José Carlos Santos, Micah, Strants Aug 3 at 14:33

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Henrik, Claude Leibovici, José Carlos Santos, Micah, Strants

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  You will find you get better help if you can show what your thoughts are, or what you've already attempted (by editing your question) :)
  – postmortes
  Aug 3 at 5:56
  

  
  
  
  


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  I am unable to get the answer
  – user581382
  Aug 3 at 5:57
  

  
  
  
  


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  Welcome to math.SE. If you describe the thoughts you've into this problem/the work you've done, we can offer help with the specific problem you're having. If you don't be prepared that the question will get closed for lack of context quite fast.
  – Henrik
  Aug 3 at 6:04
  

  
  
  
  

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up vote
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favorite

If one end of the line segment is (1, 2) and the point which divides internally in the ratio 1 : 2 is origin, find the other externally.

plane-geometry

share|cite|improve this question

asked Aug 3 at 5:54

user581382

1

put on hold as off-topic by Henrik, Claude Leibovici, José Carlos Santos, Micah, Strants Aug 3 at 14:33

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Henrik, Claude Leibovici, José Carlos Santos, Micah, Strants

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  You will find you get better help if you can show what your thoughts are, or what you've already attempted (by editing your question) :)
  – postmortes
  Aug 3 at 5:56
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I am unable to get the answer
  – user581382
  Aug 3 at 5:57
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to math.SE. If you describe the thoughts you've into this problem/the work you've done, we can offer help with the specific problem you're having. If you don't be prepared that the question will get closed for lack of context quite fast.
  – Henrik
  Aug 3 at 6:04
  

  
  
  
  

add a comment | 

up vote
-2
down vote

favorite

up vote
-2
down vote

favorite

If one end of the line segment is (1, 2) and the point which divides internally in the ratio 1 : 2 is origin, find the other externally.

plane-geometry

share|cite|improve this question

asked Aug 3 at 5:54

user581382

1

If one end of the line segment is (1, 2) and the point which divides internally in the ratio 1 : 2 is origin, find the other externally.

plane-geometry

share|cite|improve this question

asked Aug 3 at 5:54

user581382

1

share|cite|improve this question

share|cite|improve this question

asked Aug 3 at 5:54

user581382

1

asked Aug 3 at 5:54

user581382

1

asked Aug 3 at 5:54

user581382

1

1

put on hold as off-topic by Henrik, Claude Leibovici, José Carlos Santos, Micah, Strants Aug 3 at 14:33

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Henrik, Claude Leibovici, José Carlos Santos, Micah, Strants

If this question can be reworded to fit the rules in the help center, please edit the question.

put on hold as off-topic by Henrik, Claude Leibovici, José Carlos Santos, Micah, Strants Aug 3 at 14:33

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Henrik, Claude Leibovici, José Carlos Santos, Micah, Strants

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  You will find you get better help if you can show what your thoughts are, or what you've already attempted (by editing your question) :)
  – postmortes
  Aug 3 at 5:56
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I am unable to get the answer
  – user581382
  Aug 3 at 5:57
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to math.SE. If you describe the thoughts you've into this problem/the work you've done, we can offer help with the specific problem you're having. If you don't be prepared that the question will get closed for lack of context quite fast.
  – Henrik
  Aug 3 at 6:04
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  You will find you get better help if you can show what your thoughts are, or what you've already attempted (by editing your question) :)
  – postmortes
  Aug 3 at 5:56
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I am unable to get the answer
  – user581382
  Aug 3 at 5:57
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to math.SE. If you describe the thoughts you've into this problem/the work you've done, we can offer help with the specific problem you're having. If you don't be prepared that the question will get closed for lack of context quite fast.
  – Henrik
  Aug 3 at 6:04
  

  
  
  
  

You will find you get better help if you can show what your thoughts are, or what you've already attempted (by editing your question) :)
– postmortes
Aug 3 at 5:56

You will find you get better help if you can show what your thoughts are, or what you've already attempted (by editing your question) :)
– postmortes
Aug 3 at 5:56

I am unable to get the answer
– user581382
Aug 3 at 5:57

I am unable to get the answer
– user581382
Aug 3 at 5:57

Welcome to math.SE. If you describe the thoughts you've into this problem/the work you've done, we can offer help with the specific problem you're having. If you don't be prepared that the question will get closed for lack of context quite fast.
– Henrik
Aug 3 at 6:04

Welcome to math.SE. If you describe the thoughts you've into this problem/the work you've done, we can offer help with the specific problem you're having. If you don't be prepared that the question will get closed for lack of context quite fast.
– Henrik
Aug 3 at 6:04

add a comment | 

2 Answers
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Refer to the graph:

$hspace6cm$

Note that the triangles $Delta ADO$ and $Delta ABC$ are similar. Hence:
$$fracAOAB=fracADAC=fracDOBC iff frac13=frac2AC=frac1BC iff AC=6; BC=3.$$
Can you figure out the coordinates of the point $B$?

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answered Aug 3 at 14:16

farruhota

13.4k2632

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Notice that $C$ is a definite proportion point of the directed line segment $overlineAB.$ Denote the three points as $$A(x_a,y_a),B(x_b,y_b),C(x_c,y_c).$$We've known that $x_a=1,y_a=2$,$x_c=0,y_c=0$ and $lambda=dfracoverlineACoverlineCB=dfrac12.$ Thus, by the formula of definite proportion, we obtain $$fracx_a+lambda x_b1+lambda=frac1+dfrac12x_b1+dfrac12=x_c=0,~~~~fracy_a+lambda y_b1+lambda=frac2+dfrac12y_b1+dfrac12=y_c=0.$$
As a result $$x_b=-2,~~~y_b=-4.$$

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answered Aug 3 at 8:31

mengdie1982

2,840216

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
0
down vote

Refer to the graph:

$hspace6cm$

Note that the triangles $Delta ADO$ and $Delta ABC$ are similar. Hence:
$$fracAOAB=fracADAC=fracDOBC iff frac13=frac2AC=frac1BC iff AC=6; BC=3.$$
Can you figure out the coordinates of the point $B$?

share|cite|improve this answer

answered Aug 3 at 14:16

farruhota

13.4k2632

add a comment | 

up vote
0
down vote

Refer to the graph:

$hspace6cm$

Note that the triangles $Delta ADO$ and $Delta ABC$ are similar. Hence:
$$fracAOAB=fracADAC=fracDOBC iff frac13=frac2AC=frac1BC iff AC=6; BC=3.$$
Can you figure out the coordinates of the point $B$?

share|cite|improve this answer

answered Aug 3 at 14:16

farruhota

13.4k2632

add a comment | 

up vote
0
down vote

up vote
0
down vote

Refer to the graph:

$hspace6cm$

Note that the triangles $Delta ADO$ and $Delta ABC$ are similar. Hence:
$$fracAOAB=fracADAC=fracDOBC iff frac13=frac2AC=frac1BC iff AC=6; BC=3.$$
Can you figure out the coordinates of the point $B$?

share|cite|improve this answer

answered Aug 3 at 14:16

farruhota

13.4k2632

Refer to the graph:

$hspace6cm$

Note that the triangles $Delta ADO$ and $Delta ABC$ are similar. Hence:
$$fracAOAB=fracADAC=fracDOBC iff frac13=frac2AC=frac1BC iff AC=6; BC=3.$$
Can you figure out the coordinates of the point $B$?

share|cite|improve this answer

answered Aug 3 at 14:16

farruhota

13.4k2632

share|cite|improve this answer

share|cite|improve this answer

answered Aug 3 at 14:16

farruhota

13.4k2632

answered Aug 3 at 14:16

farruhota

13.4k2632

answered Aug 3 at 14:16

farruhota

13.4k2632

13.4k2632

add a comment | 

add a comment | 

up vote
-1
down vote

Notice that $C$ is a definite proportion point of the directed line segment $overlineAB.$ Denote the three points as $$A(x_a,y_a),B(x_b,y_b),C(x_c,y_c).$$We've known that $x_a=1,y_a=2$,$x_c=0,y_c=0$ and $lambda=dfracoverlineACoverlineCB=dfrac12.$ Thus, by the formula of definite proportion, we obtain $$fracx_a+lambda x_b1+lambda=frac1+dfrac12x_b1+dfrac12=x_c=0,~~~~fracy_a+lambda y_b1+lambda=frac2+dfrac12y_b1+dfrac12=y_c=0.$$
As a result $$x_b=-2,~~~y_b=-4.$$

share|cite|improve this answer

answered Aug 3 at 8:31

mengdie1982

2,840216

add a comment | 

up vote
-1
down vote

Notice that $C$ is a definite proportion point of the directed line segment $overlineAB.$ Denote the three points as $$A(x_a,y_a),B(x_b,y_b),C(x_c,y_c).$$We've known that $x_a=1,y_a=2$,$x_c=0,y_c=0$ and $lambda=dfracoverlineACoverlineCB=dfrac12.$ Thus, by the formula of definite proportion, we obtain $$fracx_a+lambda x_b1+lambda=frac1+dfrac12x_b1+dfrac12=x_c=0,~~~~fracy_a+lambda y_b1+lambda=frac2+dfrac12y_b1+dfrac12=y_c=0.$$
As a result $$x_b=-2,~~~y_b=-4.$$

share|cite|improve this answer

answered Aug 3 at 8:31

mengdie1982

2,840216

add a comment | 

up vote
-1
down vote

up vote
-1
down vote

Notice that $C$ is a definite proportion point of the directed line segment $overlineAB.$ Denote the three points as $$A(x_a,y_a),B(x_b,y_b),C(x_c,y_c).$$We've known that $x_a=1,y_a=2$,$x_c=0,y_c=0$ and $lambda=dfracoverlineACoverlineCB=dfrac12.$ Thus, by the formula of definite proportion, we obtain $$fracx_a+lambda x_b1+lambda=frac1+dfrac12x_b1+dfrac12=x_c=0,~~~~fracy_a+lambda y_b1+lambda=frac2+dfrac12y_b1+dfrac12=y_c=0.$$
As a result $$x_b=-2,~~~y_b=-4.$$

share|cite|improve this answer

answered Aug 3 at 8:31

mengdie1982

2,840216

Notice that $C$ is a definite proportion point of the directed line segment $overlineAB.$ Denote the three points as $$A(x_a,y_a),B(x_b,y_b),C(x_c,y_c).$$We've known that $x_a=1,y_a=2$,$x_c=0,y_c=0$ and $lambda=dfracoverlineACoverlineCB=dfrac12.$ Thus, by the formula of definite proportion, we obtain $$fracx_a+lambda x_b1+lambda=frac1+dfrac12x_b1+dfrac12=x_c=0,~~~~fracy_a+lambda y_b1+lambda=frac2+dfrac12y_b1+dfrac12=y_c=0.$$
As a result $$x_b=-2,~~~y_b=-4.$$

share|cite|improve this answer

answered Aug 3 at 8:31

mengdie1982

2,840216

share|cite|improve this answer

share|cite|improve this answer

answered Aug 3 at 8:31

mengdie1982

2,840216

answered Aug 3 at 8:31

mengdie1982

2,840216

answered Aug 3 at 8:31

mengdie1982

2,840216

2,840216

add a comment | 

add a comment |