Coordinate Geometry (NCERT Ch. 7)

• Find the distance between two points using the distance formula.
• Find the coordinates of a point dividing a line segment in a given ratio (section formula).
• Find the area of a triangle formed by three given points.

1. Distance formula: distance between (x₁,y₁) and (x₂,y₂) = √[(x₂-x₁)² + (y₂-y₁)²].
2. Section formula (dividing in ratio m:n): x = (mx₂+nx₁)/(m+n), y = (my₂+ny₁)/(m+n).
3. Midpoint formula (special case, ratio 1:1): x = (x₁+x₂)/2, y = (y₁+y₂)/2.
4. Area of a triangle with vertices (x₁,y₁),(x₂,y₂),(x₃,y₃) = (1/2)|x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|.

Find the distance between (2,3) and (5,7).

Distance = sqrt[(5-2)² + (7-3)²] = sqrt[9+16] = sqrt[25] = 5

• Forgetting to square the differences before adding in the distance formula.
• Mixing up the order of m and n in the section formula.
• Forgetting the absolute value (modulus) when computing triangle area (area cannot be negative).

• Find the distance between (0,0) and (3,4).
• Find the midpoint of (2,4) and (6,8).

Open the Practice tab for graded questions on Coordinate Geometry (NCERT Ch. 7).