Question

find the Centroids of the triangles
whose vertices
are given below.
(4,7),(8,4), (7,11)​

Answer 1

Step-by-step explanation:

centroid=(x1+x2+x3÷3 , y1+y2+y3÷3)

=(4+8+7÷3 , 7+4+11÷3)

=(19/3,22/3)

hope this helped you..

Answer 2

Gɪᴠᴇɴ :-

• vertices of ∆ = (4,7),(8,4), (7,11) .

Tᴏ Fɪɴᴅ :-

• vertices of centroid of ∆ ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• The centroid of a triangle whose vertices are (x1, y1), (x2, y2) and (x3, y3) has the coordinates (x1+x2+x3)/3, (y1+y2+y3)/3.

Sᴏʟᴜᴛɪᴏɴ :-

Given That :-

→ x1 = 4

→ x2 = 8

→ x3 = 7

→ y1 = 7

→ y2 = 4

→ y3 = 11

Putting values in above told formula now we get :-

→ x = (x1 + x2 + x3)/3

→ x = (4 + 8 + 7) / 3

→ x = (19/3)

And,

→ y = (y1 + y2 + y3)/3

→ y = (7 + 4 + 11) / 3

→ y = (22/3)

Hence, vertices of centroid of given ∆ are {(19/3) & (22/3)} .

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Extra :-

• Area of ∆ vertices A(x1, y1), B(x2, y2) and C(x3, y3) is :- | (1/2) [x1 (y2- y3 )+x2 (y3-y1 )+x3(y1-y2)] |

Note :- The two vertical bars means we have to use "Absolute Value". Or, it is always positive even if the formula produced a negative result. Polygons can never have a Negative Area.

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