Question

Show that the point (11, –2) is equidistant from (4, –3) and (6, 3).

Answer 1

Let P(x₁, y₁) = P(11, –2), Q(x₂, y₂) = Q(4, –3), R(x₃, y₃) = R(6, 3)

By distance formula,

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

= `sqrt((4 - 11)^2 + [-3 - (-2)]^2`

= `sqrt((-7)^2 + (-1)^2`

= `sqrt(49 + 1)`

= `sqrt(50)`

= `5sqrt(2)`

And

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

= `sqrt((6 - 11)^2 + [3 - (-2)]^2`

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

= `sqrt(25 + 25)`

= `sqrt(50)`

= `5sqrt(2)`

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

∴ Point (11, –2) is equidistant from (4, –3) and (6, 3).