The Distance Formula The Distance Formula Today we are going to discuss What is the Distance Formula between two points. We need to have the knowledge about the given two points. Suppose if we have one point as (a,b) and other point as (c,d) then we can find the distance between these two points by the formula given below, D=?(c2-a2) +(d2-b2) We denote distance by D, Now the problem is that how we can find the points(a,b) and (c,d). As we are seeing that every point has two variables, a is the distance in x direction and b is the distance in y direction similarly c is the distance in x direction and d is the distance in y direction. If we talk about space, in space one point is indicated by 2 points. As we know that distance can't be in negative, but if space comes in negative then it just indicate the direction. If we see the points (c,a) both points belongs to x, so we can call it as abscissa and points (d,b) belong to y direction, so we can call it as ordinates. Now we will see some examples to be more familiar about distance between two points.

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Example 1: find the distance between points (3,4) and (5,6) Solution :- Here points (3,4) belongs to (a,b) and (5,6) belong to (c,d), Now we need to put the given values in the formula and we simply get the desired answer. D=?(c2-a2) +(d2-b2) D=?(52-32) +(62-42) D=?(25-9) +(36-16) D= ?16+20 D=?36 D=6 So 6 is the distance between between the given points. If we have points in x axis then the points in y direction will be zero. If we have points (a,b) and (c,d) then the points b and d will be 0. Now if we are asked to calculate the distance between (a,0) and (c,0) then the distance between the given points. D= ?(0-a2)+(0-c2) D=? a2 + c2 This is the formula for distance if we have points in x axis. If we have points in y axis then the points in x direction will be zero. If we have points (a,b) and (c,d) then the points a and d will be 0. Now if we are asked to calculate the distance between (0,b) and (0,d) then the distance between the given points.

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D= ?(0-b2)+(0-d2) D=? b2 + d2 This is the formula for distance if we have points in y axis. Now we will see one example to be more clear about finding the distance in space. Example 2: find the distance between the points (3,0) and (4,0)? Solution: Now as we are seeing that points are in x direction so we will apply the given formula above D= ? 32 + 42 D= ? 9+16 D= ? 25 D=5 This is the required distance. Example 3: find the distance between the points (0,4) and (0,5)? solution: Now as we are seeing that points are in y direction so we will apply the given formula above D= ? 52 + 42 D= ? 25+16 D= ? 39

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