note: Enter your answer and show all the steps that you use to solve this problem in the space provided.Explain the distance formula. Then use it to calculate the distance between A(1, 1) and B(7,%E2%88%927).
The distance formula is a mathematical formula used to calculate the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and is expressed as:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
In this formula, (x1, y1) and (x2, y2) represent the coordinates of the two points.
To calculate the distance between A(1, 1) and B(7, -7), we can substitute the values into the distance formula and solve step by step:
Distance = √[(7 - 1)^2 + (-7 - 1)^2]
= √[(6)^2 + (-8)^2]
= √[(36) + (64)]
= √[100]
= 10
Therefore, the distance between A(1, 1) and B(7, -7) is 10 units.