# Geometry: Distance Formula

Usually the coordinate place consists of two axes namely X axis and Y axis. Thus, a point in a coordinate plane is usually denoted by the coordinates (x,y) where x is the perpendicular distance of the point from Y-axis and y is the perpendicular distance from the X-axis as shown below.
Thus we can easily find the distance of a point from the axes just by seeing the x and y coordinates. But, how to find the distance between two points when their coordinates are given? We use Pythagoras theorem to find the distance between two points.
Let P (x

_{1},y_{1}) and Q (x_{2},y_{2}) be any two points in a plane. Let us find the distance between them PQ. Then from the figure, we get PR = |x_{2}-x_{1}| and QR = |y_{2}-y_{1}|. We know that the Pythagoras theorem states, “In a right angled triangle, the square of the hypotenuse is the sum of the squares of the other two sides”.’ According to this theorem, we have PQ^{2}= PR^{2}+ QR^{2}PQ^{2}= |x_{2}-x_{1}|^{2}+ |y_{2}-y_{1}|.^{2}Taking square root on both sides, we get PQ = √(|x_{2}-x_{1}|^{2}+ |y_{2}-y_{1}|^{2}) We also offer Science tutoring, click here for more information. SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Washington visit: Tutoring in Washington.