Q1. Find the distance between (1, 2) and (4, 6).
d = √[(4−1)² + (6−2)²]
d = √[9 + 16] = √25
d = 5 units
Coordinate Geometry — Class 10
Turn geometry into arithmetic. Compute the distance and midpoint between any two points, then master the section and area formulas.
Distance formulaBetween (x₁,y₁) and (x₂,y₂): d = √[(x₂−x₁)² + (y₂−y₁)²].
Section formulaThe point dividing the join of two points in ratio m:n is ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)).
MidpointThe midpoint of (x₁,y₁) and (x₂,y₂) is ((x₁+x₂)/2, (y₁+y₂)/2).
Distance & midpoint calculator Interactive
Enter two points to get the distance between them and their midpoint.
Distance—
Midpoint x—
Midpoint y—
The distance of a point (x, y) from the origin is simply √(x² + y²).
Numericals practice Interactive
Distance-formula problems with steps.
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Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| Distance | d = √[(x₂−x₁)² + (y₂−y₁)²] |
| Midpoint | ((x₁+x₂)/2, (y₁+y₂)/2) |
| Area of triangle | ½ |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)| |
Common mistakes & exam wins
- The distance formula is just Pythagoras' theorem in disguise.
- For the midpoint, take the average of the x-coordinates and the average of the y-coordinates.
- Three points are collinear if the area of the triangle they form is 0.
Frequently asked questions
What is the distance formula?
The distance between (x₁,y₁) and (x₂,y₂) is √[(x₂−x₁)² + (y₂−y₁)²].
What is the section formula?
The point dividing the segment joining two points in ratio m:n is ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)).
How do you check if three points are collinear?
They are collinear if the area of the triangle formed by them is zero.