Question

If the distance between the points (4, p) and (1, 0) is 5, what is the value of p?

Answer 1

1. Identify the points and Formula

The distance d between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:

`d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

For the points (4, p) and (1, 0) we have:

(x₁, y₁) = (4, p)

(x₂, y₂) = (1, 0)

d = 5

2. Substitute and Simplify

Plugging these values into the formula:

`5 = sqrt((1 - 4)^2 + (0 - p)^2`

`5 = sqrt((-3)^2 + (-p)^2`

`5 = sqrt(9 + p^2)`

3. Square both sides

To remove the square root, square both sides of the equation:

`5^2 = (sqrt(9 + p^2))^2`

25 = 9 + p²

4. Solve for p

Isolate p² and solve for p:

p² = 25 – 9

p² = 16

`p = ±sqrt(16)`

p = ±4