Determine the distance between the points (2, 3) and (2, -1).

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Question: Determine the distance between the points (2, 3) and (2, -1).

Options:

Correct Answer: 4

Solution:

Using the distance formula: d = √[(2 - 2)² + (-1 - 3)²] = √[0 + 16] = √16 = 4.

Determine the distance between the points (2, 3) and (2, -1).

Determine the distance between the points (2, 3) and (2, -1).

Step 1: Identify the coordinates of the two points. The first point is (2, 3) and the second point is (2, -1).
Step 2: Write down the distance formula: d = √[(x2 - x1)² + (y2 - y1)²].
Step 3: Substitute the coordinates into the formula. Here, x1 = 2, y1 = 3, x2 = 2, and y2 = -1.
Step 4: Calculate the difference in the x-coordinates: (x2 - x1) = (2 - 2) = 0.
Step 5: Calculate the difference in the y-coordinates: (y2 - y1) = (-1 - 3) = -4.
Step 6: Square the differences: (0)² = 0 and (-4)² = 16.
Step 7: Add the squared differences: 0 + 16 = 16.
Step 8: Take the square root of the sum: √16 = 4.
Step 9: The distance between the points (2, 3) and (2, -1) is 4.

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.