SketchMath Solves Locus Questions: Equal Distance Conditions (With Examples)
Locus flashcard example: find the locus of P when PS = PT
This guide explains the visual method clearly, but students should still re-practice on fresh diagrams to build exam muscle memory.
Locus questions often feel like guesswork to HKDSE students. You are given a condition, told to imagine a "moving point," and expected to magically pull an equation out of thin air. But what if you could actually see the path being drawn?
During our March 2026 Kowloon locus drills, DSE learners tested SketchMath's interactive graphing against traditional textbook notes. The result? Watching the distance conditions update live completely removed the guesswork.
Here is how visual learning turns abstract locus definitions into solid exam marks.
A Quick Worked Example: Equal Distance Locus
Let's look at a classic DSE setup: Find the locus of a moving point P(x, y) that maintains an equal distance from two fixed points, S(2, 1) and T(8, 1).
Because P satisfies PS = PT, the point must lie on the perpendicular bisector of ST. Since S and T form a horizontal line, their midpoint is M(5, 1), making the perpendicular bisector the vertical line x = 5.
The SketchMath Advantage: Instead of just writing the equation and hoping it's right, SketchMath lets you drag point P along the line x = 5. As P moves, the platform dynamically displays the lengths of PS and PT, proving they stay perfectly equal. You get to visually confirm the locus condition before you write your final exam statement.
Click the video to explore this question interactively →
10 Steps to Master Locus Conditions
Here is the exact workflow our top students use to conquer perpendicular-bisector locus questions:
The Setup
- Locate your fixed points (S and T) on the coordinate plane.
- Move point P manually along its displayed path.
- Compare the PS and PT measurement labels at each step.
The Execution
- Check if the PS = PT equality holds true globally across the graph.
- Infer the geometric locus condition from the visual pattern.
- Relate the path you see to the perpendicular-bisector logic.
- Write a concise theorem reason for your exam paper.
The Review
- Stress-test the argument by dragging P to the extreme endpoints of the slider range.
- Convert your visual observations directly into a standard DSE exam statement.
- Hide the interactive hints and reproduce the locus from a blank sketch.
Why Interactive Graphs Beat Static Notes
1. It shows what the math actually means.
In this setup, the graph displays the intersection points S and T alongside the moving point P. As P travels along the locus line, the segment lengths PS and PT update in real time to stay equal, confirming the geometric condition dynamically.
2. It builds deep geometric intuition.
Students can verify the locus rule through physical movement instead of treating it as a blindly memorized fact. This strengthens their intuition for the perpendicular-bisector and equal-distance conditions required in Paper 1 proofs.
3. It explains the "Why", not just the "What".
Many math apps simply spit out a static equation or a dead answer line. SketchMath combines animated locus behavior with live measurements and guided explanations, helping students understand exactly why every single point on that path is valid.
What Students & Tutors Are Saying
“Moving point P manually made the condition feel provable, not magical.”
“I used the equal-distance visual as my writing scaffold.”
“Students are finally able to separate visual observations from formal theorem claims clearly.”