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If the point P(k, 4) is equidistant from the points A(2, 1) and B(8, 7), find the value of k.

Class 10Distance FormulaGeometry — Coordinates

A6
B4
C10
D5

Step-by-Step Solution

(k - 2)^{2} + (4 - 1)^{2} = (k - 8)^{2} + (4 - 7)^{2}

. So

(k - 2)^{2} + 9 = (k - 8)^{2} + 9, (k - 2)^{2} = (k - 8)^{2}

. Expand:

- 4 k + 4 = - 16 k + 64, 12 k = 60, k = 5

.

Answer: D) 5

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