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Define distance and displacement, and distinguish between the two; Solve problems involving distance and displacement
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Distance is the length of the path taken by an object whereas displacement is the simply the distance between where the object started and where it ended up. For example, lets say you drive a car. You drive it 5 miles east and then 3 miles west.
To find the distance between two points ($$x_1, y_1$$) and ($$x_2, y_2$$), all that you need to do is use the coordinates of these ordered pairs and apply the formula pictured below. The distance formula is $ \text{ Distance } = \sqrt{(x_2 -x_1)^2 + (y_2- y_1)^2} $
You have just derived the distance formula! Note that given any two points with coordinates (x1, y1) and (x2, y2), the distance, d (also called Euclidean distance), between them is given by the formula below. formula to compute the distance between the following points: 1. (1,1) and (3,7) 2. (-1,5) and (2,9)
Walk through deriving a general formula for the distance between two points. The distance between the points ( x 1, y 1) and ( x 2, y 2) is given by the following formula: ( x 2 − x 1) 2 + ( y 2 − y 1) 2. In this article, we're going to derive this formula!
Using a one-dimensional number line to visualize and calculate distance and displacement. Created by Sal Khan.
To find distance formula to calculate the distance from a point to a line in 3D, consider a point P \((x_0, y_0, z_0)\) and a line (L) in 3D whose equation is \(\dfrac{x-x_1}{a}=\dfrac{y-y_1}{b}=\dfrac{z-z_1}{c}\). Then the distance (d) from the point P to L is, \(d=\dfrac{| \overline{PQ} \times \bar{s} |}{|\bar{s}|}\), where
