Find locus of centroid of - ABC- if B 1-1-C4-2 and A lies on the line y-x-3

The correct option is D 3x 3y+1=0 Let centroid be (h,k) Let #160; point A be (p,3+p) h=1+p+43 ; k=1+2+3+p3 h=5+p3 ; k ...

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Standard VIII

Mathematics

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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x - y = 3

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3 x - 3 y + 1 = 0

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Solution

The correct option is D $3 x - 3 y + 1 = 0$
Let centroid be $(h, k)$

Let point $A$ be $(p, 3 + p)$

$h = \frac{1 + p + 4}{3}$ ; $k = \frac{1 + 2 + 3 + p}{3}$

$h = \frac{5 + p}{3}$ ; $k = \frac{6 + p}{3}$

$3 h - 5 = 3 k - 6$

put $h = x, k = y$

$3 x - 3 y + 1 = 0$

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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 D 3x−3y+1=0Let centroid be (h,k)Let point A be (p,3+p)h=1+p+43; k=1+2+3+p3h=5+p3; k=6+p33h−5=3k−6put h=x,k=y3x−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 D $3 x - 3 y + 1 = 0$
Let centroid be $(h, k)$

Let point $A$ be $(p, 3 + p)$

$h = \frac{1 + p + 4}{3}$ ; $k = \frac{1 + 2 + 3 + p}{3}$

$h = \frac{5 + p}{3}$ ; $k = \frac{6 + p}{3}$

$3 h - 5 = 3 k - 6$

put $h = x, k = y$

$3 x - 3 y + 1 = 0$