Find locus of centroid of - A B C - if B 1-1 - C 4-2 and A lies on the line y - x - 3

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The Centroid

Find locus of...

Question

Find locus of centroid of $Δ A B C,$ if $B (1, 1), C (4, 2)$ and $A$ lies on the line $y = x + 3$

3 x - 3 y + 1 = 0

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x + y = 3

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3 x - 3 y = 1 = 0

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x - y = 3

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Solution

The correct option is A $3 x - 3 y + 1 = 0$
Let the centroid be $(h, k)$
Given $B (1, 1), C (4, 2)$
So $A$ will be $(3 h - 5, 3 k - 3)$
And also $A$ lies on $y = x + 3$
$⟹ 3 k - 3 = 3 h - 5 + 3 ⟹ 3 h - 3 k + 1 = 0$
So the locus of centroid will be $3 x - 3 y + 1 = 0$

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Find locus of centroid of ΔABC, if B(1,1),C(4,2) and A lies on the line y=x+3

The correct option is A 3x−3y+1=0Let the centroid be (h,k)Given B(1,1),C(4,2)So A will be (3h−5,3k−3)And also A lies on y=x+3⟹3k−3=3h−5+3⟹3h−3k+1=0So the locus of centroid will be 3x−3y+1=0

Find locus of centroid of $Δ A B C,$ if $B (1, 1), C (4, 2)$ and $A$ lies on the line $y = x + 3$

The correct option is A $3 x - 3 y + 1 = 0$
Let the centroid be $(h, k)$
Given $B (1, 1), C (4, 2)$
So $A$ will be $(3 h - 5, 3 k - 3)$
And also $A$ lies on $y = x + 3$
$⟹ 3 k - 3 = 3 h - 5 + 3 ⟹ 3 h - 3 k + 1 = 0$
So the locus of centroid will be $3 x - 3 y + 1 = 0$