Important Notes on Distance Between Two Points: The points that denote the given complex numbers are (1, 3) and (2, -4). Here |z 1 − z 2| is the absolute value of the complex number z 1 − z 2.Įxample: Find the distance between the complex numbers z 1 = 1 3i and z 2 = 2 - 4i. Then the distance between the two complex numbers z 1 and z 2 is: Recall the fact that every complex number on a complex plane corresponds to a point on the coordinate plane. Consider two complex numbers z 1 = a ib and z 2 = c id. The distance between two points in a complex plane is found by using a formula that is similar to the distance between two points formula in cartesian plane. In the same way, the distance between two points that lie on a horizontal line is the absolute value of the difference in their x-coordinates.ĭistance Between Two Points in Complex Plane when the points are on a vertical line), we can find the distance between the two points by finding the absolute value of the difference between the y-coordinates. The distance between two points using coordinates can be given as, d = √, where (x 1, y 1) and (x 2, y 2) are the coordinates of the two points.įrom the above example, we can also observe that when the x-coordinates of the given points are the same (i.e. Note: We can apply the 3D distance formula in case the two points are given in 3D plane, d = √Įxample: Find the distance between the points with coordinates given as, A = (1, 2) and B = (1, 5). We can apply the distance formula to find the distance between the two points, d = √.Note down the coordinates of the two given points in the coordinate plane as, A(x 1, y 1) and B(x 2, y 2).The distance between two points using the given coordinates can be calculated with the help of the following given steps: How to Find Distance Between Two Points of Coordinates? Using similar steps and concepts, we can also derive the formula to find the distance between two points given in the 3D plane. the coordinates of A and B are (x 1, 0) and (x 2, 0) respectively, then the distance between two points AB = |x 2 − x 1|. Note: In case the two points A and B are on the x-axis, i.e. Thus, the distance formula to find the distance between two points is proved. ![]() The horizontal distance between the given points is |x 2 − x 1|.ĭ = √ (Taking square root on both sides) Here, the vertical distance between the given points is |y 2 − y 1|. Next, we will assume that the line segment joining A and B is \(\overline\) as the hypotenuse.Īpplying Pythagoras theorem for the △ABC:ĭ 2 = (x 2 − x 1) 2 (y 2 − y 1) 2 (Values from the figure) To derive the formula to calculate the distance between two points in a two-dimensional plane, let us assume that there are two points with the coordinates given as, A(x 1, y 1) B(x 2, y 2). Derivation of Formula for Distance Between Two Points of Coordinates
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