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VMariaS [17]
3 years ago
11

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

Mathematics
1 answer:
Pani-rosa [81]3 years ago
5 0
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

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Answer:

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Step-by-step explanation:

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d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2

Our first point, A, is at (1, 1) and our second point, B, is at (-2, 8).

Let's let A(1, 1) be (x₁, y₁) and B(-2, 8) be (x₂, y₂). Substitute this into the distance formula:

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Subtract:

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Add:

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