Question

If G and G' are the centroids of the triangles ABC and A'B'C', then `overline("A""A"^') + overline("B""B"^') + overline("C""C"^')` is equal to ______ 

पर्याय

• `overline("G""G"^')`

• 2`overline("G""G"^')`

• 3`overline("G""G"^')`

• `2/3overline("G""G"^')`

Answer 1

If G and G' are the centroids of the triangles ABC and A'B'C', then `overline("A""A"^') + overline("B""B"^') + overline("C""C"^')` is equal to `underline(3overline("G""G"^'))`.

Explanation:

`overline("A""A"^') + overline("B""B"^') + overline("C""C"^') = overline("a"^') - overline"a" + overline("b"^') - overline"b" + overline("c"^') - overline"c"`

= `(overline("a"^')  + overline("b"^') + overline("a"^') ) - (overline"a" + overline"b" + overline"c")`

= `3overline("g"^') - 3overline"g"` .....[∵ G' and G are centroids]

= 3 `overline("GG"^')`