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 ______.

विकल्प

• 7

• 7 or –5

• –1

• 1

Answer 1

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.