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Question
If the distance between the points (4, P) and (1, 0) is 5, then the value of p is ______.
Options
4 only
± 4
– 4 only
0
Solution
If the distance between the points (4, p) and (1, 0) is 5, then the value of p is ± 4.
Explanation:
According to the question,
The distance between the points (4, p) and (1, 0) = 5
d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
i.e., `sqrt((1 - 4)^2 + (0 - "p")^2` = 5
⇒ `sqrt((-3)^2 + "p"^2)` = 5
⇒ `sqrt(9 + "p"^2)` = 5
On squaring both the sides, we get
9 + p2 = 25
⇒ p2 = 16
⇒ p = ± 4
Hence, the required value of p is ± 4.
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