Question

The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x = ______.

Options

• 2

• 6

• 3

• 1

Answer 1

The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x = 6.

Explanation:

Let P(x₁, y₁) = P(2, 2) and Q(x₂, y₂) = Q(5, x)

Here, x₁ = 2, y₁ = 2, x₂ = 5, y₂ = x

By distance formula,

d(P, Q) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`

∴ `5 = sqrt((5 - 2)^2 + (x - 2)^2)`

∴ `5 = sqrt(9 + x^2 - 4x + 4)`

∴ 5² = x² – 4x + 13   ...[Squaring both sides]

∴ 25 = x² – 4x + 13 

∴ x² – 4x + 13 – 25 = 0

∴ x² – 4x – 12 = 0

∴ (x – 6) (x + 2) = 0

∴ x – 6 = 0 or x + 2 = 0

∴ x = 6 or x = –2