Question

Please solve q 76?

Answer 1

The answer is `=3`

Explanation:

Let the mid-point of `BC` be

`P(3/2,-5/2)`

and

`G(p,q)`

`A(2,1)`

Then, by the definition of the centroid

`vec(AG)/vec(AP)=2/3`

Taking the x- coordinates

`(p-2)/(3/2-2)=2/3`

`p-2=2/3*-1/2=-1/3`

`p=2-1/3=5/3`

`vec(AG)/vec(AP)=2/3`

Taking the y-coordinates

`(q-1)/(-5/2-1)=2/3`

`q-1=2/3*-7/2=-7/3`

`q=1-7/3=-4/3`

Therefore,

`p-q=5/3-(-4/3)=5/3+4/3=9/3=3`