Vectors, calculate distance from these two points [closed]

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My Attempt Thus far.. I tried using the quadratic formula on this to find the distance/magnitude , however it did not work. I then tried to solve it as a quadratic inequality.
Can anyone help?
And please I would like to know how the answer can be achieved really step by step.

The distance from point (−1, 1) to (2, −𝑠) is 5/13 of the distance from (14, 2) to
(2, −𝑠). If it is known that 𝑠 > 0, find 𝑠.

linear-algebra algebra-precalculus vector-spaces vectors quadratics

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edited Jul 22 at 15:26

asked Jul 22 at 15:16

Corey Robinson

63

closed as off-topic by amWhy, uniquesolution, José Carlos Santos, Mostafa Ayaz, Parcly Taxel Jul 24 at 15:24

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." – amWhy, uniquesolution, José Carlos Santos, Mostafa Ayaz, Parcly Taxel

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

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up vote
0
down vote

favorite

My Attempt Thus far.. I tried using the quadratic formula on this to find the distance/magnitude , however it did not work. I then tried to solve it as a quadratic inequality.
Can anyone help?
And please I would like to know how the answer can be achieved really step by step.

The distance from point (−1, 1) to (2, −𝑠) is 5/13 of the distance from (14, 2) to
(2, −𝑠). If it is known that 𝑠 > 0, find 𝑠.

linear-algebra algebra-precalculus vector-spaces vectors quadratics

share|cite|improve this question

edited Jul 22 at 15:26

asked Jul 22 at 15:16

Corey Robinson

63

closed as off-topic by amWhy, uniquesolution, José Carlos Santos, Mostafa Ayaz, Parcly Taxel Jul 24 at 15:24

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." – amWhy, uniquesolution, José Carlos Santos, Mostafa Ayaz, Parcly Taxel

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

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

My Attempt Thus far.. I tried using the quadratic formula on this to find the distance/magnitude , however it did not work. I then tried to solve it as a quadratic inequality.
Can anyone help?
And please I would like to know how the answer can be achieved really step by step.

The distance from point (−1, 1) to (2, −𝑠) is 5/13 of the distance from (14, 2) to
(2, −𝑠). If it is known that 𝑠 > 0, find 𝑠.

linear-algebra algebra-precalculus vector-spaces vectors quadratics

share|cite|improve this question

edited Jul 22 at 15:26

asked Jul 22 at 15:16

Corey Robinson

63

My Attempt Thus far.. I tried using the quadratic formula on this to find the distance/magnitude , however it did not work. I then tried to solve it as a quadratic inequality.
Can anyone help?
And please I would like to know how the answer can be achieved really step by step.

The distance from point (−1, 1) to (2, −𝑠) is 5/13 of the distance from (14, 2) to
(2, −𝑠). If it is known that 𝑠 > 0, find 𝑠.

linear-algebra algebra-precalculus vector-spaces vectors quadratics

share|cite|improve this question

edited Jul 22 at 15:26

asked Jul 22 at 15:16

Corey Robinson

63

share|cite|improve this question

share|cite|improve this question

edited Jul 22 at 15:26

edited Jul 22 at 15:26

edited Jul 22 at 15:26

asked Jul 22 at 15:16

Corey Robinson

63

asked Jul 22 at 15:16

Corey Robinson

63

asked Jul 22 at 15:16

Corey Robinson

63

63

closed as off-topic by amWhy, uniquesolution, José Carlos Santos, Mostafa Ayaz, Parcly Taxel Jul 24 at 15:24

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." – amWhy, uniquesolution, José Carlos Santos, Mostafa Ayaz, Parcly Taxel

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

closed as off-topic by amWhy, uniquesolution, José Carlos Santos, Mostafa Ayaz, Parcly Taxel Jul 24 at 15:24

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." – amWhy, uniquesolution, José Carlos Santos, Mostafa Ayaz, Parcly Taxel

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

add a comment | 

add a comment | 

2 Answers
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1
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accepted

Step 1: compute the square of the first distance, a quadratic polynomial in s.

Step 2: compute the square of the second distance, a quadratic polynomial in s.

Step 3: express that the first squared distance is the second squared distance times a known constant.

Step 4: move all terms to the same member.

Step 5: solve the quadratic equation.

Step 6: discard the negative solution.

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answered Jul 22 at 15:34

Yves Daoust

111k665203

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0
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Since you said you used the quadratic formula, perhaps you made a math error. As the comment says, please show more of your work. You can learn mathjax here which is similar to latex.

Here is the worked out answer.

$$ sqrt(2-(-1))^2 + (-s-1)^2 = frac513 sqrt(2-14)^2 + (-s-2)^2 $$
$$ sqrt9 + s^2+2s+1 = frac513 sqrt144 + s^2+4s+4 $$
$$ sqrts^2+2s+10 = frac513 sqrts^2+4s+148 $$

$$ s^2+2s+10 = frac25169 cdot left(s^2+4s+148right) $$

$$ 169s^2 + 338s + 1690 = 25s^2 + 100s + 3700 $$

$$ 144s^2 + 238s - 2010 =0 $$

$$ 72s^2 + 119s - 1005 =0 $$

Quadratic formula:

$$ frac-119 pm sqrt119^2-4cdot72 cdot (-1005)144$$

$$ frac-119 pm 551144 $$

We want only the positive $s$ so:

$$ frac432144 $$

$$ s=3 $$

share|cite|improve this answer

answered Jul 22 at 15:54

Dan Sp.

27919

add a comment | 

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote



accepted

Step 1: compute the square of the first distance, a quadratic polynomial in s.

Step 2: compute the square of the second distance, a quadratic polynomial in s.

Step 3: express that the first squared distance is the second squared distance times a known constant.

Step 4: move all terms to the same member.

Step 5: solve the quadratic equation.

Step 6: discard the negative solution.

share|cite|improve this answer

answered Jul 22 at 15:34

Yves Daoust

111k665203

add a comment | 

up vote
1
down vote



accepted

Step 1: compute the square of the first distance, a quadratic polynomial in s.

Step 2: compute the square of the second distance, a quadratic polynomial in s.

Step 3: express that the first squared distance is the second squared distance times a known constant.

Step 4: move all terms to the same member.

Step 5: solve the quadratic equation.

Step 6: discard the negative solution.

share|cite|improve this answer

answered Jul 22 at 15:34

Yves Daoust

111k665203

add a comment | 

up vote
1
down vote



accepted

up vote
1
down vote



accepted

Step 1: compute the square of the first distance, a quadratic polynomial in s.

Step 2: compute the square of the second distance, a quadratic polynomial in s.

Step 3: express that the first squared distance is the second squared distance times a known constant.

Step 4: move all terms to the same member.

Step 5: solve the quadratic equation.

Step 6: discard the negative solution.

share|cite|improve this answer

answered Jul 22 at 15:34

Yves Daoust

111k665203

Step 1: compute the square of the first distance, a quadratic polynomial in s.

Step 2: compute the square of the second distance, a quadratic polynomial in s.

Step 3: express that the first squared distance is the second squared distance times a known constant.

Step 4: move all terms to the same member.

Step 5: solve the quadratic equation.

Step 6: discard the negative solution.

share|cite|improve this answer

answered Jul 22 at 15:34

Yves Daoust

111k665203

share|cite|improve this answer

share|cite|improve this answer

answered Jul 22 at 15:34

Yves Daoust

111k665203

answered Jul 22 at 15:34

Yves Daoust

111k665203

answered Jul 22 at 15:34

Yves Daoust

111k665203

111k665203

add a comment | 

add a comment | 

up vote
0
down vote

Since you said you used the quadratic formula, perhaps you made a math error. As the comment says, please show more of your work. You can learn mathjax here which is similar to latex.

Here is the worked out answer.

$$ sqrt(2-(-1))^2 + (-s-1)^2 = frac513 sqrt(2-14)^2 + (-s-2)^2 $$
$$ sqrt9 + s^2+2s+1 = frac513 sqrt144 + s^2+4s+4 $$
$$ sqrts^2+2s+10 = frac513 sqrts^2+4s+148 $$

$$ s^2+2s+10 = frac25169 cdot left(s^2+4s+148right) $$

$$ 169s^2 + 338s + 1690 = 25s^2 + 100s + 3700 $$

$$ 144s^2 + 238s - 2010 =0 $$

$$ 72s^2 + 119s - 1005 =0 $$

Quadratic formula:

$$ frac-119 pm sqrt119^2-4cdot72 cdot (-1005)144$$

$$ frac-119 pm 551144 $$

We want only the positive $s$ so:

$$ frac432144 $$

$$ s=3 $$

share|cite|improve this answer

answered Jul 22 at 15:54

Dan Sp.

27919

add a comment | 

up vote
0
down vote

Since you said you used the quadratic formula, perhaps you made a math error. As the comment says, please show more of your work. You can learn mathjax here which is similar to latex.

Here is the worked out answer.

$$ sqrt(2-(-1))^2 + (-s-1)^2 = frac513 sqrt(2-14)^2 + (-s-2)^2 $$
$$ sqrt9 + s^2+2s+1 = frac513 sqrt144 + s^2+4s+4 $$
$$ sqrts^2+2s+10 = frac513 sqrts^2+4s+148 $$

$$ s^2+2s+10 = frac25169 cdot left(s^2+4s+148right) $$

$$ 169s^2 + 338s + 1690 = 25s^2 + 100s + 3700 $$

$$ 144s^2 + 238s - 2010 =0 $$

$$ 72s^2 + 119s - 1005 =0 $$

Quadratic formula:

$$ frac-119 pm sqrt119^2-4cdot72 cdot (-1005)144$$

$$ frac-119 pm 551144 $$

We want only the positive $s$ so:

$$ frac432144 $$

$$ s=3 $$

share|cite|improve this answer

answered Jul 22 at 15:54

Dan Sp.

27919

add a comment | 

up vote
0
down vote

up vote
0
down vote

Since you said you used the quadratic formula, perhaps you made a math error. As the comment says, please show more of your work. You can learn mathjax here which is similar to latex.

Here is the worked out answer.

$$ sqrt(2-(-1))^2 + (-s-1)^2 = frac513 sqrt(2-14)^2 + (-s-2)^2 $$
$$ sqrt9 + s^2+2s+1 = frac513 sqrt144 + s^2+4s+4 $$
$$ sqrts^2+2s+10 = frac513 sqrts^2+4s+148 $$

$$ s^2+2s+10 = frac25169 cdot left(s^2+4s+148right) $$

$$ 169s^2 + 338s + 1690 = 25s^2 + 100s + 3700 $$

$$ 144s^2 + 238s - 2010 =0 $$

$$ 72s^2 + 119s - 1005 =0 $$

Quadratic formula:

$$ frac-119 pm sqrt119^2-4cdot72 cdot (-1005)144$$

$$ frac-119 pm 551144 $$

We want only the positive $s$ so:

$$ frac432144 $$

$$ s=3 $$

share|cite|improve this answer

answered Jul 22 at 15:54

Dan Sp.

27919

Since you said you used the quadratic formula, perhaps you made a math error. As the comment says, please show more of your work. You can learn mathjax here which is similar to latex.

Here is the worked out answer.

$$ sqrt(2-(-1))^2 + (-s-1)^2 = frac513 sqrt(2-14)^2 + (-s-2)^2 $$
$$ sqrt9 + s^2+2s+1 = frac513 sqrt144 + s^2+4s+4 $$
$$ sqrts^2+2s+10 = frac513 sqrts^2+4s+148 $$

$$ s^2+2s+10 = frac25169 cdot left(s^2+4s+148right) $$

$$ 169s^2 + 338s + 1690 = 25s^2 + 100s + 3700 $$

$$ 144s^2 + 238s - 2010 =0 $$

$$ 72s^2 + 119s - 1005 =0 $$

Quadratic formula:

$$ frac-119 pm sqrt119^2-4cdot72 cdot (-1005)144$$

$$ frac-119 pm 551144 $$

We want only the positive $s$ so:

$$ frac432144 $$

$$ s=3 $$

share|cite|improve this answer

answered Jul 22 at 15:54

Dan Sp.

27919

share|cite|improve this answer

share|cite|improve this answer

answered Jul 22 at 15:54

Dan Sp.

27919

answered Jul 22 at 15:54

Dan Sp.

27919

answered Jul 22 at 15:54

Dan Sp.

27919

27919

add a comment | 

add a comment |