Find the distance between the points (-1, -1) and (2, 2).

Find the distance between the points (-1, -1) and (2, 2).

Step 1: Identify the coordinates of the two points. The first point is (-1, -1) and the second point is (2, 2).
Step 2: Use the distance formula, which is d = √[(x2 - x1)² + (y2 - y1)²]. Here, (x1, y1) = (-1, -1) and (x2, y2) = (2, 2).
Step 3: Substitute the values into the formula. So, d = √[(2 - (-1))² + (2 - (-1))²].
Step 4: Simplify the expressions inside the parentheses. This gives us d = √[(2 + 1)² + (2 + 1)²] = √[3² + 3²].
Step 5: Calculate the squares. This results in d = √[9 + 9].
Step 6: Add the results inside the square root. So, d = √18.
Step 7: Simplify √18. This can be written as √(9 * 2) = √9 * √2 = 3√2.

Distance Formula – The distance between two points in a Cartesian plane is calculated using the formula d = √[(x2 - x1)² + (y2 - y1)²].
Coordinate Geometry – Understanding how to plot points and calculate distances in a two-dimensional space.