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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
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Solution
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 7 or –5.
Explanation:
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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