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If the vertices P, Q, R are rational poi...

If the vertices `P, Q, R` are rational points which of the following points of the triangle `P Q R` is (are) always rational point(s)?

A

centroid

B

incentre

C

circumcentre

D

orthocentre

Text Solution

Verified by Experts

The correct Answer is:
A
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Knowledge Check

  • Let A = (p, q, r) which of the following is an equvilance relation on A?

    A
    `R_{1} = {(p, q), (q, r), (p, r), (p, p)}`
    B
    `R_{2} = {(r, p ), (q, p ), (r, r), (q, q)}`
    C
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    D
    `R_{4} = {(p, p), (q, q), (r, r)}`

  • If p, q, r are real numbers then:

    A
    max. (p, q) `lt` max. (p, q, r)
    B
    min. `(p, q)=(1)/(2)(p+q-|p-q|)`
    C
    min. (p, q) = min. (p, q, r)
    D
    None of these

  • Let S be a non-empty subset of R . Consider the following statement P: There is a rational number x in S such that x>0 which of the following statement is the negation of the statement P.

    A
    Every rational number x in S satisfies` x leq 0`
    B
    x in S and` x leq 0 rarr x` is not rational
    C
    There is a rational number x in S such that` x leq 0`
    D
    There is no rational number x in S such that` x leq 0`

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