Examine whether the points (1, - 1), (- 5, 7) and (2, 6) are equidistant from the point (- 2, 3)?

Given that we need to show that the points (1, - 1), (- 5, 7) and (2, 6) are equidistant from the point (- 2, 3).

We know that distance between two points (x₁, y₁) and (x₂, y₂) is

Let S₁ be the distance between the points (1, - 1) and (- 2, 3)

⇒ S_{1 =} 5 ..... (1)

Let S₂ be the distance between the points (- 5, 7) and (- 2, 3)

⇒ S_{2 =} 5 ..... (2)

Let S₃ be the distance between the points (2, 6) and (- 2, 3)

⇒ S_{3 =} 5 ..... (3)

From (1), (2), and (3) we got S_{1 =} S_{2 =} S₃ which tells us that (1, - 1), (5, 7) and (2, 5) are equidistant from (- 2, 3).