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Class 10 Coordinate Geometry: cheat sheet
CBSE Mathematics. Points on a plane: the distance between two points, and the point that divides a line segment in a given ratio.
Key ideas
- The distance formula comes from Pythagoras: the horizontal and vertical gaps are the two legs.
- A point dividing AB in the ratio m : n (inside AB) is found with the section formula.
- The midpoint is the section formula with m = n = 1.
- Three points A, B, C lie on one line when the two shorter distances add up to the longest.
- To show a quadrilateral is a square, rhombus or rectangle, compare its sides and diagonals using the distance formula.
Remember
| Distance between (x₁, y₁) and (x₂, y₂) | √((x₂ − x₁)² + (y₂ − y₁)²) |
| Distance from the origin | √(x² + y²) |
| Section formula (m : n) | ((mx₂ + nx₁) ÷ (m + n), (my₂ + ny₁) ÷ (m + n)) |
| Midpoint | ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2) |
Watch out
- Swapping m and n in the section formula: m goes with the second point (x₂, y₂).
- Forgetting that the square of a negative difference is positive.
- Stopping at (x₂ − x₁)² + (y₂ − y₁)² and forgetting the square root.
Worked example
Show that A(−5, 6), B(1, 12), C(−5, 18) and D(−11, 12) form a square, and find its area.
Working: AB² = 6² + 6² = 72 for every side; equal diagonals make it a square
Answer: all sides 6√2, both diagonals 12; area 72 square units
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