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If the point P(k-1, 2) is equidistan...

If the point `P(k-1, 2)` is equidistant from the points `A(3, k)` and `B(k , 5)` , find the values of `k` .

A

k=2

B

k=5

C

k=0

D

k=-1

Text Solution

Verified by Experts

The correct Answer is:
B
It is being given that P(k-1, 2) is equidistant from the points A(3, k) and B(k, 5). So, we have
`PA = PB rArr PA^(2) = PB^(2)`
`rArr (k-1-3)^(2) + (2-k)^(2) = (k-1-k)^(2) + (2-5)^(2)`
`rArr (k-4)^(2) + (2-k)^(2) = (-1)^(2) + (-3)^(2)`
`rArr 2k^(2)-12k +20 = 1+9 rArr 2k^(2) -12k +10=0`
`rArr k^(2)-6k+5 = 0rArr k^(2) - 5k-k+5=0`
`rArr k(k-5) - (k-5) = 0 rArr (k-5) (k-1) = 0`
`rArr k= 1 "or" k = 5`
Hence, the required values of k are 1 and 5
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