Page 1 Coordinate Geometry Page 2 Coordinate Geometry Distance Formula : 1 1 2 2 Distance between two points (x ,y ) & (x ,y ) Section Formula : Internal division P (x, y) = m 1 x 2 + m 2 x 1 m 1 + m 2 m 1 y 2 + m 2 y 1 m 1 + m 2 { , } External division m 1 x 2 - m 2 x 1 m 1 - m 2 { , m 1 y 2 - m 2 y 1 m 1 - m 2 } Mid point { , } P (x, y) = x 1 + x 2 2 y 1 + y 2 2 Area of triangle : A = {x 1 (y 2 - y 3 ) + x 2 (y 3 - y 1 ) + x 3 (y 1 - y 2 )} 1 2 D = v (x 1 -x 2 ) 2 + (y 1 -y 2 ) 2 D = v (x 2 -x 1 ) 2 + (y 2 -y 1 ) 2 or P (x, y) = Coordinate axes x axis y axis . . . . (+, -) (-, -) (+, +) 1 st Quadrant 2 nd Quadrant 3 rd Quadrant 4 th Quadrant (-, +) = = = COORDINATE GEOMETRY 20 Coordinate Geometry Page 3 Coordinate Geometry Distance Formula : 1 1 2 2 Distance between two points (x ,y ) & (x ,y ) Section Formula : Internal division P (x, y) = m 1 x 2 + m 2 x 1 m 1 + m 2 m 1 y 2 + m 2 y 1 m 1 + m 2 { , } External division m 1 x 2 - m 2 x 1 m 1 - m 2 { , m 1 y 2 - m 2 y 1 m 1 - m 2 } Mid point { , } P (x, y) = x 1 + x 2 2 y 1 + y 2 2 Area of triangle : A = {x 1 (y 2 - y 3 ) + x 2 (y 3 - y 1 ) + x 3 (y 1 - y 2 )} 1 2 D = v (x 1 -x 2 ) 2 + (y 1 -y 2 ) 2 D = v (x 2 -x 1 ) 2 + (y 2 -y 1 ) 2 or P (x, y) = Coordinate axes x axis y axis . . . . (+, -) (-, -) (+, +) 1 st Quadrant 2 nd Quadrant 3 rd Quadrant 4 th Quadrant (-, +) = = = COORDINATE GEOMETRY 20 Coordinate Geometry To check whether the three points form an isosce- les triangle or an equilateral triangle, nd out the distance between all the three points and if the two sides or three sides are same, we can con- clude the answer respectively. To check whether the three points A, B and C are collinear either show AB + BC = AC or you can prove it by calculating the area of a triangle formed by these three points is zero. To calculate the area of any quadrilateral, divide it into two triangles then nd the area of individual triangle and add them. ? ? Please try to remember all the properties of quadrilaterals and triangles, for the questions which ask to check whether the points form any geometrical shape or not. ? ? PLEASE KEEP IN MIND Scan the QR Codes to watch our free videos Introduction to Coordinate Geometry Distance formula COORDINATE GEOMETRY 21Read More

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