❖ Learn how to find the Radius and Area of a Circle using the distance between two points in \(2D\) in this beginner-friendly coordinate geometry lesson!

We use the distance between two points (\(C\) and \(P\)) on the \(xy\)-plane to get the radius, then compute the area with \(A = \pi r^2\). Clear, step-by-step example.

🎯 Key concepts covered:

– Distance formula in \(2D\):

$$d = \sqrt{((x₂ − x₁)^2 + (y₂ − y₁)^2}$$

– Center \(C\) to point \(P\) on the circle gives the radius (\(d = r\))

– Area of a circle: \(A = \pi r^2\)

– Plotting points and reading coordinates on the \(xy\)-plane

✔️ What this lesson includes:

– Quick refresher of the distance formula

– Find the radius r using the distance formula from \(C(−1,1)\) to \(P(3,4)\)

– Area calculation: \(A = r^2 \pi \) with \(r=5\)

– Sketching the circle using \(r = 5\) (up/down/left/right)

🎯 Whether you’re a student, teacher, or math enthusiast, this lesson will help you apply the distance formula with confidence to find a circle’s radius and area.

✨ Watch next:

🔹 Distance Formula: Radius and Volume of a Solid Sphere