Question

ABC is a triangle and G (4,3) is the centroid of the traingle. If A, B and C are the points (1,3),(4,b) and (a,1) respectively, find the values of a and b. Also find the length of side BC.

Answer 1

A= (1,3)
B= (4,b)
C= (a,1)
& G= (4,3)   ....... (1)

Formula of Centroid-
$x_{1}+ x_{2}+ x_{3}$ /3 , $y_{1} +y_{2} +y_{3}$ /3

Therefore,
(1+4+a)/3 , (3+b+1)/3
(5+a)/3 , (4+b)/3 ......(2)

On comparing (1) & (2),
(5+a)/3=4
5+a=12
a=7
&
(4+b)/3=3
4+b=9
b=5

Answer 2

Answer:

Step-by-step explanation:

A= (1,3)

B= (4,b)

C= (a,1)

& G= (4,3)   ....... (1)

Formula of Centroid-

/3 , /3

Therefore,

(1+4+a)/3 , (3+b+1)/3

(5+a)/3 , (4+b)/3 ......(2)

On comparing (1) & (2),

(5+a)/3=4

5+a=12

a=7

&

(4+b)/3=3

4+b=9

b=5

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