Final answer:
To calculate the distance between the points (5, 2) and (-5, 6), the distance formula is used, yielding a result of approximately 10.77 units.
Step-by-step explanation:
To find the distance between two points (5, 2) and (-5, 6) on the Cartesian plane, you can use the distance formula derived from the Pythagorean theorem. The distance between two points is the length of the line joining the two points. If the two points lie on the same horizontal or same vertical line, the distance can be found by subtracting the coordinates that are not the same.
In analytic geometry, distance formula is used to find the distance measure between two lines, the sum of the lengths of all the sides of a polygon, perimeter of polygons on a coordinate plane, the area of polygons and many more. For example, we can find the lengths of the sides of a triangle using the distance formula and determine whether the triangle is scalene, isosceles or equilateral.
The distance formula is √((x2 - x1)2 + (y2 - y1)2). Substituting the x and y values of the points into the formula gives us:
√((-5 - 5)2 + (6 - 2)2) = √((-10)2 + (4)2) = √(100 + 16) = √(116) = 10.77 (rounded to two decimal places).
Therefore, the distance traveled between the two points is approximately 10.77 units.