Question

Show that the point (0, 9) is equidistant from the points (–4, 1) and (4, 1).

Answer 1

Let P(x₁, y₁) = P(0, 9), Q(x₂, y₂) = Q(–4, 1), R(x₃, y₃) = R(4, 1)

By distance formula,

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

= `sqrt([(-4) - 0]^2 + (1 - 9)^2`

= `sqrt((-4)^2 + (-8)^2`

= `sqrt(16 + 64)`

= `sqrt(80)`

= `4sqrt(5)`

And

d(P, R) = `sqrt((x_3 - x_1)^2 + (y_3 - y_1)^2`

= `sqrt((4 - 0)^2 + (1 - 9)^2`

= `sqrt(4^2 + (-8)^2`

= `sqrt(16 + 64)`

= `sqrt(80)`

= `4sqrt(5)`

Here, d(P, Q) = d(P, R)

∴ The point (0, 9) is equidistant from (–4, 1) and (4, 1).