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Teaching video
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Grade 10 chapters and video availability01 · Read and understand
What you will learn
- Derive a perpendicular bisector as an equidistance locus.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Algebraic equations, ratios, angle and area facts, and basic coordinate geometry.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Find all points (x,y) equally distant from A=(−2,0) and B=(4,0).
Why this math matters
Use intersections of equidistance loci to locate a circle center. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use Euclidean geometry and the angle, parallelism, similarity, or congruence conditions stated; a sketch alone does not establish them.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Find points equally distant from two endpoints
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Find all points (x,y) equally distant from A=(−2,0) and B=(4,0).
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the conditions
(x+2)²+y²=(x−4)²+y²
Equal distances have equal squared distances.
Develop the calculation
x²+4x+4=x²−8x+16
The common y² and x² terms cancel.
Check and interpret
x=1, with any real y
This vertical line passes through the midpoint (1,0) and is perpendicular to AB.
The result
x=1, with any real y
This vertical line passes through the midpoint (1,0) and is perpendicular to AB.
Common mistakes to catch
- A perpendicular bisector is a line, not merely a midpoint.
- Equidistance concerns the two specified endpoints, not every point of the segment.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Where is the circumcenter of the right triangle (0,0),(6,0),(0,8)?
Show a hint
Intersect the perpendicular bisectors x=3 and y=4.
Reveal answer and explanation
(3,4)
Its distance to each vertex is five, so it is the common circle center.
Practice 2
Does the perpendicular bisector consist only of the segment midpoint?
Show a hint
The equidistance equation leaves y unrestricted here.
Reveal answer and explanation
No
Every point on the entire perpendicular line is equally distant from the endpoints.
Take the idea with you
Use intersections of equidistance loci to locate a circle center.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Connect a circle's central and inscribed angles
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