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Suppose A(2,3,7), B(-1,3,2) and C(p,s,r)...

Suppose A(2,3,7), B(-1,3,2) and C(p,s,r) are the vertices of `DeltaABC`. If the median through A is equally inclined to the corrdinate axes then the cooprdinate of the vertec C is

A

(7,5,12)

B

(7,5,16)

C

(7,5,14)

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let D be the mid-point of BC
`therefore" "D=((-1+p)/2,(3+5)/2,(2+r)/2)`
`=((-1+p)/2,4,(2+r)/2)`
Now DR's of AD are `((-1+p)/2-2,4-3,(2+r)/2-7)`
i.e `((p-5)/2,1,(r-12)/2)`
Since, the line AD is equally inclined to the coordinate axes. Therefore DR's of AD are (1,1,)
`((p-5)/2)/1=1/1=((r-12)/2)/1`
`rArr" "(p-5)/2=1 and (r-12)/2=1`
`rArr" "p=7 and r=14`
`therefore` Coordinates of C (7,5,14)
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