Question

If the distance between the points (4, p) and (1, 0) is 5, then p is equal to ______.

Options

• ±4

•  4

•  –4

•  0

Answer 1

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