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Quantitative Aptitude

Triangles

In ABC, A≡1,1...

Question

In $△ A B C, A \equiv (1, 1)$ and $P, Q, R$ are respectively the midpoints of sides $B C, C A$ and $A B$ where $P \equiv (- 3, - 1)$ . If centroid of $△ P Q R$ is $(α, β)$ then $| α + β |$

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Solution

The correct option is C $2$
Centroid of $△ A B C$ divides $A P$ in the ratio $2 : 1$
$∴ G \equiv (\frac{- 5}{3}, \frac{- 1}{3})$
We know that centroid of triangle and triangle formed by its midpoints are same.
$∴$ centroid of $△ P Q R \equiv (α, β) \equiv (\frac{- 5}{3}, \frac{- 1}{3})$
$\Rightarrow | α + β | = 2$

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In △ABC,A≡(1,1) and P,Q,R are respectively the midpoints of sides BC,CA and AB where P≡(−3,−1). If centroid of △PQR is (α,β) then |α+β|

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