Question

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

Answer 1

Here is your answer.....

Answer 2

Solution:

It is being given that P(k-1, 2) is equidistant from the points

A(3, k) and B(k, 5).

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So, we have

⇒ PA = PB

⇒ PA² = PB²

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⇒ (k-1-3)² + (2-k)² = (k-1-k)² + (2-5)²

⇒ (k-4)² + (2-k)² = (-1)² + (-3)²

⇒ 2k² - 12k + 20 = 1 + 9

⇒ 2k² - 12k + 10 = 0

⇒k²- 6k + 5 = 0

⇒k² - 5k - k + 5 = 0

⇒ k(k-5) - (k-5) = 0

⇒(k-5)(k-1) = 0

⇒ k = 1 or k = 5.

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Hence, the required values of k are 1 and 5.

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Answer:-

• The value of k = 1 or 5.