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Question
If the distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x.
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Solution
Let L(x1, y1) = L(x, 7) and M(x2, y2) = M(1, 15)
x1 = x, y1 = 7, x2 = 1, y2 = 15
By distance formula,
d(L, M) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
∴ d(L, M) = `sqrt((1 - x)^2 + (15 - 7)^2`
∴ `10 = sqrt((1 - x)^2 + 8^2`
∴ 100 = (1 – x)2 + 64 ...[Squaring both sides]
∴ (1 – x)2 = 100 – 64
∴ (1 – x)2 = 36
∴ `1 - x = ± sqrt(36)` ...[Taking square root of both sides]
∴ 1 – x = ± 6
∴ 1 – x = 6 or 1 – x = – 6
∴ x = –5 or x = 7
∴ The value of x is –5 or 7.
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