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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
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Solution
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
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