Midpoint intuition in coordinates
The midpoint is the point exactly halfway between two endpoints of a segment.
In one line: Halfway means average both coordinates.
Practice This ConceptUnderstand it
In coordinate geometry, the midpoint is found by averaging the x-coordinates and the y-coordinates separately. This works because the halfway point must split both the horizontal and vertical changes equally. The midpoint formula gives an exact answer, even if the segment lies in any quadrant.
Formula and rule
Midpoint = ((x1 + x2)/2, (y1 + y2)/2).
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
For (2, -1) and (8, 5), midpoint = ((2 + 8)/2, (-1 + 5)/2) = (5, 2).
Method you can reuse
- 1Add the two x-coordinates.
- 2Divide by 2.
- 3Add the two y-coordinates.
- 4Divide by 2.
- 5Write the midpoint as an ordered pair.
Visual tip
On the graph, the midpoint must sit exactly halfway along the segment in both directions.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
What is the midpoint of (2, -1) and (8, 5)?
Think first, then show answerHide answer
Common wrong answer
A common wrong answer is (6, 4), because students move halfway by eye instead of averaging the coordinates exactly.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
The midpoint is the point exactly halfway between two endpoints of a segment.
- 2
Add for 2 marks
Example: The midpoint of (2, -1) and (8, 5) is (5, 2).
- 3
Add for 3 marks
In coordinate geometry, the midpoint is found by averaging the x-coordinates and the y-coordinates separately.
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