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If the point P(k-1, 2) is equidistant from the points A(3, k)

Question

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

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Oliver Discussed

If the point

P (k - 1, 2)

is equidistant from the points

A (3, k)

and

B (k, 5)

, find the values of k.

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Point P

(k - 1, 2)

is equidistant from the points A

(3, k)

and B

(k, 5)

P A = PB

P A^{2} = P B^{2}

\Rightarrow (3 - k + 1)^{2} + (k - 2)^{2} = (k - k + 1)^{2} + (5 - 2)^{2}

\Rightarrow (4 - k)^{2} + (k - 2)^{2} = 1^{2} + 3^{2}

\Rightarrow 16 - 8 k + k^{2} + k^{2} - 4 k + 4 = 1 + 9

\Rightarrow 2 k^{2} - 12 k + 20 = 10

\Rightarrow 2 k^{2} - 12 k + 20 - 10 = 0

\Rightarrow 2 k^{2} - 12 k + 10 = 0

\Rightarrow k^{2} - 6 k + 5 = 0

\Rightarrow k^{2} - k - 5 k + 5 = 0

\Rightarrow k (k - 1) - 5 (k - 1) = 0

\Rightarrow (k - 5) (k - 1) = 0

k = 1

k = 5

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Question Text	If the point $P (k - 1, 2)$ is equidistant from the points $A (3, k)$ and $B (k, 5)$ , find the values of k.
Answer Type	Text solution:1
Upvotes	150