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Question
If the length of the segment joining point L(x, 7) and point M(1, 15) is 10 cm, then the value of x is ______
Options
7
7 or – 5
–1
1
Solution
7 or – 5
Here, 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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