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Question
If the distance between the points (4, p) and (1, 0) is 5, then p is equal to ______.
Options
±4
4
–4
0
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Solution
If the distance between the points (4, p) and (1, 0) is 5, then p is equal to ±4.
Explanation:
It is given that distance between P(4, p) and Q(1, 0) is 5.
In general, the distance between A(x1, y1) and B(x2, y2) is given by,
d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
So, `sqrt((1 - 4)^2 + (0 - "p")^2` = 5
⇒ `sqrt((-3)^2 + "p"^2)` = 5
⇒ `sqrt(9 + "p"^2)` = 5
On further simplification,
9 + p2 = 25
p2 = 16
p = ±4
So, p = ±4
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