Find the distance between the points (5, 5) and (5, 1).

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Question: Find the distance between the points (5, 5) and (5, 1).

Options:

Correct Answer: 4

Solution:

Using the distance formula: d = √[(5 - 5)² + (1 - 5)²] = √[0 + 16] = √16 = 4.

Find the distance between the points (5, 5) and (5, 1).

Find the distance between the points (5, 5) and (5, 1).

Step 1: Identify the coordinates of the two points. The first point is (5, 5) and the second point is (5, 1).
Step 2: Write down the distance formula: d = √[(x2 - x1)² + (y2 - y1)²].
Step 3: Assign the coordinates to the formula. Here, x1 = 5, y1 = 5, x2 = 5, and y2 = 1.
Step 4: Substitute the values into the formula: d = √[(5 - 5)² + (1 - 5)²].
Step 5: Calculate (5 - 5) which equals 0, and (1 - 5) which equals -4.
Step 6: Square the results: (0)² = 0 and (-4)² = 16.
Step 7: Add the squared results together: 0 + 16 = 16.
Step 8: Take the square root of 16: √16 = 4.
Step 9: The distance between the points (5, 5) and (5, 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].
Vertical Distance – When points have the same x-coordinate, the distance is simply the absolute difference between their y-coordinates.