Distance Formula | MathHelp.com

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In this example, we’re asked to find the distance between the points (1, 2) and (5, -1), so we use the distance formula, which states that the distance between two points is equal to the square root of parentheses x2 minus x1 squared + parentheses y2 - y1 squared. Our first point, (1, 2), represents (x1, y1), and our second point, (5, -1), represents (x2, y2). So plugging the given information into the formula, we have the square root of parentheses x2, which is 5, minus x1, which is 1, squared, minus parentheses y2, which is -1, minus y1, which is 2, squared. Next, we simplify inside the parentheses. 5 – 1 is 4, and – 1 – 2 is -3, so we have the square root of 4 squared plus -3 squared. Next, 4 squared is 16, and -3 squared is positive 9, so we have the square root of 16 plus 9, or the square root of 25, which is 5. So the distance between the points (1, 2) and (5, -1) is 5.