What is the distance between the points (-2,1) and (3,7)

Distance ≈ 7.8

Step-by-step explanation:

The distance between two points in a coordinate plane can be found by forming a right triangle and using the Pythagorean Theorem to find the distance.  Pythagorean Theorem has the following formula:  a² + b² = c², where 'a' and 'b' are the legs of the triangle and 'c' is the hypotenuse, or the distance between the given points.  In this case, the distance on the 'x' axis (from -2 to 3) is 5 and the distance on the 'y' axis (from 1 to 7) is 6.  When we put these values into the equation:  5² + 6² = c² or 25 + 36 = c²

61 = c²  so, take the square root of each side:  √62 = √c²  or c ≈ 7.8

you need a common difference between consecutive terms to be constant, like 1,2,3,4 or 2,4,6,8, or 1,3,6,9