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# Distance between Two Points

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 Sub Topics The distance between two points is given by $D = \sqrt{dp^2 + dq^2}$.Here, ‘D’ is the distance. ‘P’ is the coordinates of x - axis. ‘Q’ is the coordinates of y - axis.‘dp’ is the difference between the x - coordinates of the points.‘dq’ is the difference between the y - coordinates of the points. Suppose we have coordinates of the points, then we use the above formula for finding the distance between the coordinates of the points. In other words, the length of the line segment is also said to be the distance of a line or the distance from a point to a line when the coordinates are $(p_1, q_1)$ and $(p_2, q_2)$.Then, the distance between two points given their coordinates is given by the pythagoras theorem as follows:$D = \sqrt{(p_2 - p_1)^2 + (q_2 - q_1)^2}$.For three coordinates (p_1, q_1, r_1) and (p_2, q_2, r_2), then the distance between three points is given as follows:$D = \sqrt{(p_2 - p_1)^2 + (q_2 - q_1)^2 + (r^2 - r^1)^2}$.And, in general, the distance between two points ‘p’ and ‘q’ is given by: D = |p – q| Suppose we have the coordinates points (5, 8) and (-9, -3), then let us find the distance between these two points. We know that the coordinates of the points is $(p_1, q_1)$ and $(p_2, q_2)$. Here, $p_1 = 5$$p_2 = -9$$q_1 = 8$$q_2 = -3$ Then, the distance between the two points is:$D = \sqrt{(p_2 - p_1)^2 + (q_2 - q_1)^2}$ Then, put the values in the given formula: $D = \sqrt{(-9 - 5)^2 + (-3 - 8)^2}$ On further solving, we getD = $\sqrt{(14)^2 + (-11)^2}$D = $\sqrt{196 + 121}$D = $\sqrt{317}$D = 17.80 So, the distance from the point to the line is 17.80.