What quantity did you change?
Labs / Mathematics
Distance & Locus
A circle is not just a round shape — it is every point that sits the same distance from a center. Drag the center, set a radius, and move the test point P around to watch its distance change and see exactly when it lands inside, on, or outside the circle.
Labs / Mathematics / Distance & Locus
Distance & Locus
A circle is not just a round shape — it is every point that sits the same distance from a center. Drag the center, set a radius, and move the test point P around to watch its distance change and see exactly when it lands inside, on, or outside the circle.
Why it matters
Why explore this?
Mathematics helps us describe patterns precisely and predict what comes next. This model turns an abstract relationship into something you can change and observe.
Explore
Try the model
eq x² + y² = 9|CP| 4.47 uP is OUTSIDE
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- Where does P have to be for its distance to exactly equal the radius — and how many such points are there?
- Slide the center off the origin. How do the numbers inside the equation (x − h)² + (y − k)² = r² change?
- Turn on the distance formula. Can you see how Δx and Δy build a right triangle whose hypotenuse is |CP|?
- Keep P fixed and grow the radius. At what value does P flip from outside to inside?
- Can you place C and P so that |CP| is a whole number even though neither Δx nor Δy is zero?
Explain
Make sense of what happened
State the pattern in words, test it with another example, and then connect it to the mathematical rule or representation shown in the model.
Check
Before you leave
What pattern did you observe?
Does the pattern work for another example?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.