Math Is Fun Forum

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: 10 second questions

Hi;

Why is it that whenever I do this by finding the distance between points using Pythagoras, I always get an answer very close to but not quite consistent with the formula?

Last edited by Relentless (2016-01-08 03:18:49)

zetafunc

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Registered: 2014-05-21

Posts: 2,432

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Re: 10 second questions

Why is it that whenever I do this by finding the distance between points using Pythagoras, I always get an answer very close to but not quite consistent with the formula?

I don't think it is a right-angled triangle.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: 10 second questions

Hi zetafunc, no the triangle is acute, but the distance formula essentially uses Pythagoras by creating an artificial right triangle with the desired distance as the hypotenuse.
If I calculate the distance between (-5,-1) and (5,2) it is sqrt109 ~ 10.44, I will call that the base. I then note that the midpoint is (0,1/2), I calculate the distance between that and the third point (3,-5) and I get 1/2 * sqrt157 ~ 6.265, I call that the height.

1/2 * base * height gives 1/4 * sqrt17113 ~ 32.7

But a specific formula for these things gives exactly 32, and so does Heron's formula. Maybe I have not defined the height properly or something...

I don't know about your answer

Edit: Oh I am a twit sometimes. Of course I didn't define the height properly. It has nothing to do with the midpoint

Last edited by Relentless (2016-01-08 07:25:30)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: 10 second questions

Hi bobbym, zetafunc, and Relentless,

The solution # 5634 is correct! Excellent, bobbym, zetafunc, and Relentless!

#5635. In each of the following, find the value of 'k' for which the given points are collinear:

(i) (2,-5), (3,-4), and (9,k)
(ii) (k,k), (2,3), and (4,-1)

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: 10 second questions

Hi;

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: 10 second questions

Hi Relentless and bobbym,

The solution #5635 (two parts) is perfect! Marvelous!

#5636.  Vertices of the triangle taken in order are their areas are given below. Find the value of 'a'.
(a,a), (4,5), (6,-1); Area : 9 square units.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: 10 second questions

Hi bobbym,

The solution #5636 is correct! Neat work!

#5637. Find the area of the quadrilateral formed by the points (-4,-2), (-3,-5), (3,-2), and (2,3).

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: 10 second questions

Hello;

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: 10 second questions

Hi Relentless and bobbym,

The solution #5637 is correct! Marvelous, Relentless and bobbym!

#5638. Find the area of the quadrilateral whose vertices are (6,9), (7,4), (4,2), and (3,7).

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: 10 second questions

Hi bobbym,

The solution #5638 is correct! Excellent!

#5639. Find the slope of the straight line passing through the points

.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: 10 second questions

Hi bobbym,

The solutions in #5639 (three parts) are correct! Excellent!

#5640. Using the concept of slope, show that each of the following set of points are collinear:
(i) (2,3), (3,-1), and (4,-5)
(ii) (4,1), (-2,-3), and (-5,-5).

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: 10 second questions

Hi bobbym,

The two parts of the solution #5640 are correct! Excellent!

#5641. The line joining the points A (-2,3) and B (a,5) is parallel to the line joining the points C (0,5) and D (-2,1). Find the value of 'a'.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: 10 second questions

Hi bobbym,

The solution #5641 is correct! Good work!

#5642. The line joining the points A (0,5), and B (4,2) is perpendicular to the line joining the points C (-1,-2), and D (5,b). Find the value of 'b'.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: 10 second questions

Hi bobbym,

#5643. A triangle has vertices (6,7), (2,-9), and (-4,1). Find the slopes of its medians.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: 10 second questions

Hi bobbym,

#5644. Find the equation of straight line whose angle of inclination is 45 degrees and y-intercept is 2/5.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.