Given orthocentre H-and circumcentre C-for a triangle as 2-3-and-4-5k-Then-the-centroid of triangle can be given by-

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Ratios of Distances between Centroid, Circumcenter, Incenter and Orthocenter of Triangle

Given orthoce...

Question

Given orthocentre $¯ H$ and circumcentre $¯ C$ for a triangle as $2^i + 3^j a n d 4^i + 5^k$ .Then the centroid of triangle can be given by,

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Solution

The correct option is A
We know that the centroid divides the distance between the orthocenter and circumcentre in the ratio 2:1.
$∴ C e n t r o i d = \frac{2 ¯ C + ¯ H}{3} = \frac{2 (4^i + 5^k) + 2^i + 3^j}{3} = \frac{10^i + 13^j}{3}$
Therefore correct option is a.

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Similar questions

Q. Write the coordinates of the circumcentre of a triangle whose centroid and orthocentre are at (3, 3) and (−3, 5), respectively.

Q. Given orthocentre

¯ H

and circumcentre

¯ C

for a triangle as

2^i + 3^j a n d 4^i + 5^k

.Then the centroid of triangle can be given by,

Q. Assertion(A): If centroid and circumcentre of a triangle are known its orthocentre can be found.
Reason (R) : Centriod, orthocentre and circumcentre of a triangle are collinear

Statement 1: If the vertices of a triangle are having rational coordinates, then its centroid, circumcentre and orthocentre are rational.

Statement 2: In any triangle, orthocentre, centroid and circumcentre are collinear and centroid divides the line joining orthocentre and circumcentre in the ratio $2 : 1$ .

Q. Given position vectors

¯ a, ¯ b, ¯ c

of points A, B, C for a triangle. The centroid can be given by

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Given orthocentre ¯H and circumcentre ¯C for a triangle as 2^i+3^j and 4^i+5^k.Then the centroid of triangle can be given by,

The correct option is A We know that the centroid divides the distance between the orthocenter and circumcentre in the ratio 2:1. ∴ Centroid =2¯C+¯H3=2(4^i+5^k)+2^i+3^j3=10^i+13^j3 Therefore correct option is a.

Given orthocentre $¯ H$ and circumcentre $¯ C$ for a triangle as $2^i + 3^j a n d 4^i + 5^k$ .Then the centroid of triangle can be given by,

The correct option is A
We know that the centroid divides the distance between the orthocenter and circumcentre in the ratio 2:1.
$∴ C e n t r o i d = \frac{2 ¯ C + ¯ H}{3} = \frac{2 (4^i + 5^k) + 2^i + 3^j}{3} = \frac{10^i + 13^j}{3}$
Therefore correct option is a.