Calculate the distance between the points (1, 2) and (1, 5).

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Question: Calculate the distance between the points (1, 2) and (1, 5).

Options:

Correct Answer: 3

Solution:

Using the distance formula: d = √[(1 - 1)² + (5 - 2)²] = √[0 + 9] = √9 = 3.

Calculate the distance between the points (1, 2) and (1, 5).

Calculate the distance between the points (1, 2) and (1, 5).

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

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.