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In triangle ABC, AB= AC, B :(3,6) and C:(7,12). G is the centroid of the triangle. G moves on a line x - y = 1. Find coordinates of G.

Mathematics
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I got x = 8, y =7. But getting different answer for centroid coordinate by using the centroid formula. Answer is given as G:(8,7). Can anyone explain how it is so?
Hmm wait. lemme check.
|dw:1334301435972:dw| now find h.

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Other answers:

But why do we need to find "h"?
@gurvinder please help me.
|dw:1334301902590:dw| |dw:1334302004278:dw| |dw:1334302147733:dw|
hmmm When you are using the centroid formula, you are accounting for the fact that it lies on the line but it may also lie lie outside the triangle, by distance formula. something like this. this explains the 'other' answer |dw:1334301731285:dw| so unless you put the constraint that it lies on th eline. you are have two loci of 'G'.
|dw:1334302353359:dw|
@Aadarsh .find h and find G coordinate(h+1,h).
Thanks @Taufique , @apoorvk , @gurvinder bhai for help. I got it.
since coordinate of G on the line x-y=1. hence let y coordinate=h of centroid. x-h=1. there fore x=h+1..hence it will be x coordinate of the centroid.
Thanks. i got it. Samajh mein aa gaya.
Aadarsh vai ap bht jaldi samajte hain hehe.
Aadarsh coordinate geometry ache se padhna ..
Ji haan. aur bhi ache se practice karunga.

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