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

Answer 1

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.