[MAA_96]

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

[elldeegee]

what have you done so far?

[SummerAnthems]

At least try it before coming on tsr with your homework questions... Why should we do it for you?

[MAA_96]

"Sigh" this is not a homework

[MAA_96]

I found 4) and 1) i need just a little hint for 2) and 3)

[elldeegee]

again, what have you done so far?

i have no idea what 2) is asking.
hint for q3 = cosine rule

[MAA_96]

For 1)

[z0tx]

(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:

Show

Call the centroid .

Median from

Median from

Median from

[MAA_96]

(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 ?

[z0tx]

(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:



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.

[z0tx]

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?

[MAA_96]

Nice,but why did you choose centroid here?

[z0tx]

(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).

[MAA_96]

Alright,thank you.