Coordinate Geometry Notes: Class 10 Maths Chapter 7
Class 10 Maths Chapter 7 Coordinate Geometry covers the distance formula, section formula, and the formula for the area of a triangle formed by three given points.
Overview of Topics & Subtopics (Click to Jump)
1. Distance Formula
Short Note:
• The distance between two points P(x1, y1) and Q(x2, y2) is PQ = √[(x2−x1)² + (y2−y1)²].
• Distance of a point P(x, y) from the origin O(0,0) is OP = √(x² + y²).
2. Section Formula
Short Note:
• The coordinates of the point P(x, y) which divides the line segment joining A(x1,y1) and B(x2,y2) internally in the ratio m1:m2 are: x = (m1x2+m2x1)/(m1+m2), y = (m1y2+m2y1)/(m1+m2).
• Mid-point Formula (special case with ratio 1:1): Mid-point = [(x1+x2)/2, (y1+y2)/2].
3. Area of a Triangle
Short Note:
• The area of a triangle formed by the points (x1,y1), (x2,y2), (x3,y3) is Area = ½ |x1(y2−y3) + x2(y3−y1) + x3(y1−y2)|.
• If the area of a triangle formed by three points is 0, the points are collinear.