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A(9,2) B(1,6)
if (2,k) is equidistant from A and B, find the value of k.

Sagot :

Pepe11idn
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

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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