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Triangle

Given the three points A (3,4,0) , B (8,0,6) , C (0,5,12) in space . find
1)Area of the triangle ABC
2)the length of the three medians of this triangle
3)The measure of the angle ABC
4)Equation of the plane ABC
Reply 1
Avatar for elldeegee
elldeegee
19
what have you done so far?
At least try it before coming on tsr with your homework questions... Why should we do it for you?
Reply 3
Avatar for MAA_96
MAA_96
OP
"Sigh" this is not a homework
Reply 4
Avatar for MAA_96
MAA_96
OP
I found 4) and 1) i need just a little hint for 2) and 3)
Reply 5
Avatar for elldeegee
elldeegee
19
again, what have you done so far?

i have no idea what 2) is asking.
hint for q3 = cosine rule
Reply 6
Avatar for MAA_96
MAA_96
OP
For 1)
Reply 7
Avatar for z0tx
z0tx
12
Original post by MAA_96

2)the length of the three medians of this triangle


Start by finding the coordinates of the centroid...

You should know what to do next.

If not:

Spoiler

(edited 11 years ago)
Reply 8
Avatar for MAA_96
MAA_96
OP
Original post by z0tx
Start by finding the coordinates of the centroid...


Do i have to use midpoint and use the distance formula or...to find that ?
Reply 9
Avatar for z0tx
z0tx
12
Original post by MAA_96
Do i have to use midpoint and use the distance formula or...to find that ?


Nope, midpoints would be a waste of time.

The coordinates of the centroid are:

I(13(xa+xb+xc),13(ya+yb+yc),13(za+zb+zc))I\left(\dfrac{1}{3}(x_a+x_b+x_c),\dfrac{1}{3}(y_a+y_b+y_c), \dfrac{1}{3}(z_a+z_b+z_c)\right)

Keep that in mind for future problems involving triangles!

Also, in case you don't know: the median is 3/2 of the distance between the vertex in question and the centroid.
(edited 11 years ago)
Reply 10
Avatar for z0tx
z0tx
12
I should that yes, you could find the three midpoints and calculate the three distances, but why do something thrice when you can do it once? :wink:
(edited 11 years ago)
Reply 11
Avatar for MAA_96
MAA_96
OP
Nice,but why did you choose centroid here?
Reply 12
Avatar for z0tx
z0tx
12
Original post by MAA_96
Nice,but why did you choose centroid here?


I just told you. Finding the centroid (i.e. a single point) is quicker than finding all the midpoints (i.e. three points).
Reply 13
Avatar for MAA_96
MAA_96
OP
Alright,thank you.

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