If $A (5, - 1), B (- 3, - 2)$ and $C (- 1, 8)$ are the vertices of triangle $A B C$ , find the length of median through $A$ and the coordinates of the centroid.

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Solution

$C e n t r o i d = (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3}) = (\frac{1}{3}, \frac{5}{3})$

Distance between $A$ and centroid is $\frac{2 \sqrt{65}}{3}$
Since centroid divides median in the ratio $2 : 1$
length of median $= \frac{3}{2} \times$ $\frac{2 \sqrt{65}}{3}$ $= \sqrt{65}$

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[4 MARKS]

△ A B C

is a triangle with vertices

A = (x, x + 3), B = (2, 1)

and

C = (3, - 2)

. Area of the triangle is

5

Coordinates of the centroid of

△ A B C

are

Q. In triangle

A B C

, the coordinates of vertices

A

B

and

C

are

(4, 7)

(- 2, 3)

and

(0, 1)

respectively. Find the equations of the medians passing through the vertices

A

B

and

C

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If A(5,−1),B(−3,−2) and C(−1,8) are the vertices of triangle ABC, find the length of median through A and the coordinates of the centroid.

Centroid=(x1+x2+x33,y1+y2+y33)=(13,53)Distance between A and centroid is 2√653Since centroid divides median in the ratio 2:1length of median=32× 2√653 =√65

If $A (5, - 1), B (- 3, - 2)$ and $C (- 1, 8)$ are the vertices of triangle $A B C$ , find the length of median through $A$ and the coordinates of the centroid.