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P is the point (2,k) PA = PB PA = √(49 + (2-k)²) and PB = √(1 + (6 - k)²) √(49 + (2-k)²) = √(1 + (6 - k)²) => (49 + (2-k)² = (1 + (6 - k)² => 49 + 4 - 4k + k² = 1 + 36 - 12k + k² => 8k = 37 - 53 = -16 => k = -2

Answered by pepe11 | 2024-06-10

The **value **of K is -2 if (2,k) is **equidistant **from A and B, after applying the **distance **formula.
What is a distance formula?
It is defined as the **formula **for finding the **distance **between two points. It has given the **shortest **path **distance **between two points.
P is the point (2,k)
PA = PB
PA = √(49 + (2-k)²) and PB = √(1 + (6 - k)²)
√(49 + (2-k)²) = √(1 + (6 - k)²)
=> (49 + (2-k)² = (1 + (6 - k)²
=> 49 + 4 - 4k + k² = 1 + 36 - 12k + k²
=> 8k = 37 - 53 = -16
=> k = -2
Thus, the **value **of K is -2 if (2,k) is **equidistant **from A and B, after applying the **distance **formula.
Learn more about the **distance formula **here:
brainly.com/question/18296211
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Answered by shivishivangi1679 | 2024-06-16

The value of k is -2 when the point (2, k) is equidistant from A(9, 2) and B(1, 6). By applying the distance formula and equating the distances from both points, we can solve for k. Through calculation, we find k = -2.
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Answered by shivishivangi1679 | 2024-09-04