Determine the distance between the points (0, 0) and (0, 8).

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Question: Determine the distance between the points (0, 0) and (0, 8).

Options:

Correct Answer: 8

Solution:

Using the distance formula: d = √[(0 - 0)² + (8 - 0)²] = √[0 + 64] = √64 = 8.

Determine the distance between the points (0, 0) and (0, 8).

Determine the distance between the points (0, 0) and (0, 8).

Step 1: Identify the coordinates of the two points. The first point is (0, 0) and the second point is (0, 8).
Step 2: Write down the distance formula: d = √[(x2 - x1)² + (y2 - y1)²].
Step 3: Substitute the coordinates into the formula. Here, x1 = 0, y1 = 0, x2 = 0, and y2 = 8.
Step 4: Calculate the differences: (x2 - x1) = (0 - 0) = 0 and (y2 - y1) = (8 - 0) = 8.
Step 5: Square the differences: (0)² = 0 and (8)² = 64.
Step 6: Add the squared differences: 0 + 64 = 64.
Step 7: Take the square root of the sum: √64 = 8.
Step 8: Conclude that the distance between the points (0, 0) and (0, 8) is 8.

Distance Formula – The distance between two points in a Cartesian plane is calculated using the formula d = √[(x2 - x1)² + (y2 - y1)²].
Coordinate System – Understanding the Cartesian coordinate system and how to identify points based on their (x, y) coordinates.