How do I find all the points on a Cartesian Plane that are exactly 5 units from a given coordinate, such as (3,1)

Question

I got given this question in my maths class. I know it uses the formula for distance on a Cartesian Plane but I'm unsure how to work this question out

Answer 1

Let the point (x, y) be the point(s) that are 5 units away from the point (3, 1). Then by the distance formula, we have:

√[(x - 3)² + (y - 1)²] = 5

Squaring both sides, we get

(x - 3)² + (y - 1)² = 25

Thus, any point that fits this equation, will be 5 units away from the point (3,1)

In other words, any point along the circle with a radius of 5, and a center at (3, 1)

Hope this helps.

Mr. K

Answer 2

The set of points with the given condition is the circle centered at (3,1) with radius 5.

To find an equation of the circle, we can use the distance formula:

Let (x, y) be a point on the circle.

Then √[(x-3)² + (y-1)²] = 5

Square both sides to get (x - 3)² + (y - 1)² = 25