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

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Question: Determine the distance between the points (-1, -1) and (2, 2).

Options:

Correct Answer: 5

Solution:

Using the distance formula: d = √[(2 - (-1))² + (2 - (-1))²] = √[(2 + 1)² + (2 + 1)²] = √[9 + 9] = √18 = 3√2 ≈ 4.24.

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

Determine 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: Write down the distance formula: d = √[(x2 - x1)² + (y2 - y1)²].
Step 3: Assign the values from the points to the formula. Here, x1 = -1, y1 = -1, x2 = 2, and y2 = 2.
Step 4: Substitute the values into the formula: d = √[(2 - (-1))² + (2 - (-1))²].
Step 5: Simplify the expressions inside the parentheses: d = √[(2 + 1)² + (2 + 1)²].
Step 6: Calculate the values: d = √[3² + 3²].
Step 7: Calculate 3²: d = √[9 + 9].
Step 8: Add the results: d = √[18].
Step 9: Simplify √18: d = √(9 * 2) = √9 * √2 = 3√2.
Step 10: If needed, calculate the approximate value: 3√2 ≈ 4.24.

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.