Rashmi Kathuria’s Math class mathclass_khms@yahoo.co.in
COORDINATE GEOMETRY Important points 1.The coordinates of any general point on the x-axis (x, 0). 2.The coordinates of any general point on y-axis (0,y ). 3. The distance between two points P(X1 ,Y1 ) and Q(X2 ,Y2 ) is given by the distance formula PQ = (X2 -X1 )2 + (Y2 -Y1 )2 . 4.In order to prove ,the three given points A(x1 ,y1 ),B(x2 ,y2 ) and C(x3 ,y3 ) are the vertices of an equilateral triangle, show that AB=BC=CA. 5.In order to prove the three given points A(x1 ,y1 ),B(x2 ,y2 ) and C(x3 ,y3 ) are the vertices of an isosceles triangle show that any two sides are equal . 6. In order to prove, the three given points A(x1 ,y1 ),B(x2 ,y2 ) and C(x3 ,y3 ) are the vertices of a right triangle, show that the sides verifies the Pythagoras theorem . 7.In order to prove the four given points points A(x1 ,y1 ),B(x2 ,y2 ) , C(x3 ,y3 ) and D(x4 ,y4 ) are the vertices of the square, show that AB=BC=CD=DA and diagonals AC=BD. 8. In order to prove the four given point A(x1 ,y1 ),B(x2 ,y2 ) , C(x3 ,y3 ) and D(x4 ,y4 ) are the vertices of the a rectangle show that both pairs of opposite sides are equal and diagonals AC=BD. 9.In order to prove the four given point A(x1 ,y1 ),B(x2 ,y2 ) , C(x3 ,y3 ) and D(x4 ,y4 ) are the vertices of a rhombus show that AB=BC=CD=DA . 10. In order to prove the four given point A(x1 ,y1 ),B(x2 ,y2 ) , C(x3 ,y3 ) and D(x4 ,y4 ) are the vertices of a parallelogram show that both pair of opposite sides are equal . 11.The coordinates of the point P(x ,y) which divides the join of A(x1 ,y1 ),B(x2 ,y2 ) in the ratio l: m is given by the section formula x = (lx2 +mx1 )/ (l +m) y= (ly2 +my1 )/ (l +m) 12.The coordinates of mid-point of a line segment joining A (x1 ,y1 ) ,B(x2 ,y2 ), is given by the mid-point formula x=(x1 +x2 )/2 y= (y1 +y2 )/2 13. In order to prove the given 3 points A(x1 ,y1 ),B(x2 ,y2 ) and C(x3 ,y3 ) are collinear prove AB+BC=AC . 14.The area of a triangle with vertices A(x1 ,y1 ),B(x2 ,y2 ) and C(x3 ,y3 ) is given by formula
Rashmi Kathuria’s Math class mathclass_khms@yahoo.co.in
Area triangle ABC=1/2 {x1 (y2 -y3 ) +x2 (y3 -y1 ) +x3 (y1 -y2 )} 15.Three points A(x1 ,y1 ),B(x2 ,y2 ) and C(x3 ,y3 ) are collinear if the area of triangle formed by them is zero. Area triangle ABC=1/2 {x1 (y2 -y3 ) +x2 (y3 -y1 ) +x3 (y1 -y2 )} =0 Remember area is never negative.