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Question
Find x if distance between points L(x, 7) and M(1, 15) is 10.
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Solution 1
L(x, 7), M(1, 15), and LM = 10.
By distance formula,
∴ LM = `sqrt((x − 1)^2 + (7 − 15)^2)`
∴ 10 = `sqrt((x - 1)^2 + (− 8)^2)`
Squaring both the sides, we get,
∴ 100 = (x − 1)2 + 64
∴ (x − 1)2 = 100 − 64
∴ (x − 1)2 = 36
Taking square roots of both the sides,
∴ x − 1 = `+-` 6
∴ x − 1 = 6 or x - 1 = −6
∴ x = 6 + 1 or x = −6 + 1
∴ x = 7 or x = −5
x = 7 or x = −5
Solution 2
L(x, 7), M(1, 15), and LM = 10.
By distance formula,
∴ LM = `sqrt((x − 1)^2 + (7 − 15)^2)`
∴ 10 = `sqrt((x - 1)^2 + (− 8)^2)`
Squaring both the sides, we get,
∴ 100 = (x − 1)2 + 64
∴ 100 = x2 − 2x + 1 + 64
∴ 100 = x2 − 2x + 65
∴ x2 − 2x + 65 − 100 = 0
∴ x2 − 2x − 35 = 0
∴ x2 − 7x + 5x - 35 = 0
∴ x(x − 7) + 5(x − 7) = 0
∴ (x − 7)(x + 5) = 0
∴ x − 7 = 0 or x + 5 = 0
∴ x = 7 or x = −5
x = 7 or x = −5
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