Question

A(3,-1),B(1,3),C(2,4) are vertices of ∆ABC, if D is centroid of ∆ABC and P is point of intersection of lines x+3y-1=0 and 3x-y+1=0 then which of the following points lies on line joining D and P.

A)(-9,-7),
B(-9,-6),
C(9,6),
D(9,-6)


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Answer 1

Step-by-step explanation:

Let A(3,−1),B(1,3) and C(2,4)

C(centroid)=(33+1+2,3−1+3+4)

C=(2,2)

′P′ point of intersection of lines x+3y−1=0...(i) and 3x−y+1=0...(ii)

⇒P(5−1,52)≡(x1,y1) and C(2,2)≡(x2,y2)

Ceq of line passing through C and P

Slope m=5−1−252−2=−11/5−8/5=118

⇒(y−2)=118(x−2)

⇒8x−11y+6=0

∴ (−9,−6) is the only point which satisfies the equation

Hence option ′D′ is the answer.

Answer 2

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Centroid of Δ = (2, 2) line passing through intersection of x + 3y - 1 = 0 and 3x - y + 1 = 0, be given by (x + 3y - 1) + λ(3x - y + 1) = 0 If passes through (2, 2)

⇒ 7 + 5λ = 0 

⇒ λ = - 7/5

∴ Required line is 8x - 11y + 6 = 0

∵ (-9, - 6) satisfies this equation.

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