Distance Between Two Points
The distance between two points (x1, y1) and (x2, y2) is the length of the straight line segment joining them on the Cartesian plane.
Practice This ConceptMain explanation
Teacher explanation
The distance formula comes from Pythagoras theorem. The horizontal difference is x2 - x1 and the vertical difference is y2 - y1. These act like the two perpendicular sides of a right triangle, and the required distance is the hypotenuse.
Example
Distance between (1, 2) and (4, 6) is sqrt((4 - 1)^2 + (6 - 2)^2) = sqrt(9 + 16) = 5 units.
Simple analogy
Difference, square, add, root.
Common confusion
Students sometimes add coordinates directly instead of subtracting corresponding coordinates.
Exam tip
Always subtract x-coordinates together and y-coordinates together; the squares make the final distance non-negative.
Study the distance between two points diagram carefully
Use the labelled diagram to keep distance between two points clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of distance between two points in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on distance between two points.
Revision cue
Revise distance between two points through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of distance between two points in one clean line.
2-mark use
Define distance between two points and add one example or condition.
3-mark use
Explain distance between two points, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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