Distance formula geometry1/18/2024 ![]() ![]() Since none of the points that make side a do not change their position in relation to the y axis, the distance between them is simply the difference in size of the x- coordinates of the endpoints. For clarity, let us call the line along the x-axis side a, and the line parallel to the y axis side b. ![]() The length of a leg of the triangle in a coordinate system is the distance between two points in space that are the endpoints of that particular line. The square of the length of the hypotenuse is the sum of squares of the lengths of both legs. This is the basis of the distance formula. ![]() If you do, you probably remember that the length of the hypotenuse in a right triangle can be calculated using the formula: If not, click on the Pythagorean theorem and refresh your memory. Now, you probably remember the Pythagorean theorem from the last lesson. The line that connects your point and O is the hypotenuse of said triangle and the other two lines are the legs. You should notice that the line you just drew, together with the part of the x-axis and the line connecting your point to the point of origin, forms a right triangle. Do you see it? If not, draw a line passing through the point you selected that is perpendicular to the horizontal x-axis. Now draw a line connecting that point with the point of origin. Like this:ĭraw a point in two dimensional Cartesian space. To do this, it uses the Pythagorean theorem and its properties. The distance formula helps you calculate how far apart two points in a coordinate system are. ![]()
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