10 second questions

Relentless · 2016-01-08 03:15:15

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 · 2016-01-08 05:06:40

Relentless wrote:

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 · 2016-01-08 06:54:17

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 · 2016-01-08 18:09:10

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)

Relentless · 2016-01-08 18:34:31

Hi;

bobbym · 2016-01-08 18:46:11

Hi;

Jai Ganesh · 2016-01-09 19:27:57

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.

bobbym · 2016-01-09 19:45:39

Hi;

Jai Ganesh · 2016-01-10 17:54:53

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).

Relentless · 2016-01-10 18:52:12

Hello;

bobbym · 2016-01-10 19:21:55

Hi;

Jai Ganesh · 2016-01-11 22:23:10

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).

bobbym · 2016-01-12 00:07:37

Hi;

Jai Ganesh · 2016-01-12 17:57:48

Hi bobbym,

The solution #5638 is correct! Excellent!

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

.

bobbym · 2016-01-12 19:49:08

Hi;

Jai Ganesh · 2016-01-13 18:44:49

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).

bobbym · 2016-01-13 21:27:18

Hi;

Jai Ganesh · 2016-01-14 23:37:27

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'.

bobbym · 2016-01-15 00:37:32

Hi;

Jai Ganesh · 2016-01-15 13:48:09

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'.

bobbym · 2016-01-16 08:44:29

Hi;

Jai Ganesh · 2016-01-16 15:51:18

Hi bobbym,

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

bobbym · 2016-01-16 21:00:50

Hi;

Jai Ganesh · 2016-01-17 02:30:31

Hi bobbym,

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

bobbym · 2016-01-17 04:25:12

Hi;

Math Is Fun Forum

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