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October 22, 2014

October 22, 2014

Posted by **Anonymous** on Saturday, February 2, 2013 at 8:11am.

- maths -
**bobpursley**, Saturday, February 2, 2013 at 9:31ama. Find the equation of the line BC, given two points (B and c)

Then, find the perpendicular (given the negative inverse slope from a), adn the point A.

Area? Area=lengthBC*lengthperpendicular*1/2

Just finding the area, there are other ways easier.

Graph it, use Pick's Theorem http://en.wikipedia.org/wiki/Pick%27s_theorem

or

http://www.mathopenref.com/coordtrianglearea.html

or to check your answer ONLY: http://www.gottfriedville.net/mathtools/triarea.html

- maths -
**Reiny**, Saturday, February 2, 2013 at 9:36amconsider BC as your base:

BC = √(5^2 + (-3)^2) = √34

slope of BC = -3/5

so the slope of the perpendicular = 5/3

equation of line from A to BC , using A as the point

y-3 = (5/3)(x-2)

3y - 9 = 5x - 10

5x - 3y = 1 ---- #1

equation of BC , using C

y-2 = -(3/5)(x+1)

5y - 10 = -3x -3

3x + 5y = 7 ----#2

5 times #1 --- 25x - 15y = 5

3 times #2 --- 9x + 15y = 21

add them

34x = 26

x = 26/34 = 13/17 .... ughh

in #2

3(13/17) + 5y = 7

..

y = 16/17 , yuk, the point on BC = (13/17 , 16/17)

so length of altitude

= √(2-13/17)^ + (3-16/17)^2)

= √(441/289 + 1125/289) = √(1666/289)

= 7√34/17

so the area = (1/2) base x heigh

= (1/2) * √34 * (7/17)√34 = 7 , yeahhhh

There are of course much easier ways to find the area of a triangle if you are given the three points.

The simplest way is to list the 3 points in a column repeating the first one you listed.

2 3

4 -1

-1 2

2 3

area = (1/2) | ( sum of downproducts - sum of upproducts)|

= (1/2)|(-2+ 8 - 3 -(12 + 1 + 4)|

= (1/2)| -14 |

= 7

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