Graph Universe

  Distance between two points Consider two A(x1,y1), B(x2,y2) points in the coordinate system. Distance between these two points is given by the formula, We can prove the formula by using Pythagoras Theorem From Pythagoras Theorem, Square of hypotenuse is equal to sum of squares of sides. Therefore, we get, Example: Find the distance between the points (1,2) and (-4,-3) Solution: Distance is given by

  Straight Line A Straight line is a line joining two points. Suppose there are two points A(x1,y1) and B(x2,y2) in the coordinate system. Then, the Equation of the line joining A and B is given by y-y1=m(x-x1) where m is the slope of the line AB. m is given by m=(y2-y1)/(x2-x1). An example of straight line is given below. Example: There are two points namely P(1,2) and Q(3,-8). Give the equation of the line joining the two points. Solution: As discussed above,  The line joining two points is given by y-y1=m(x-x1) First, we need to calculate slope of the line m=(-8-2)/(3-1)=-10/2=-5 => y-2=-5(x-1) => y-2=-5x+5 => 5x+y-7=0 Therefore, Equation of the line joining P and Q is given by  5x+y-7=0 General equation of a straight line is given by y=ax+b Condition for the lines to be parallel If the two lines    and    are parallel, then Condition for the lines to be perpendicular If the two lines    and    are p...