If the coordinates of point A are (2, 3) and point B are (5, 7), what is the dis

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Question: If the coordinates of point A are (2, 3) and point B are (5, 7), what is the distance between points A and B?

Options:

Correct Answer: 5 units

Solution:

Using the distance formula, d = √[(x2 - x1)² + (y2 - y1)²] = √[(5 - 2)² + (7 - 3)²] = √[3² + 4²] = √25 = 5 units.

If the coordinates of point A are (2, 3) and point B are (5, 7), what is the distance between points A and B?

If the coordinates of point A are (2, 3) and point B are (5, 7), what is the distance between points A and B?

Step 1: Identify the coordinates of point A, which are (2, 3). Here, x1 = 2 and y1 = 3.
Step 2: Identify the coordinates of point B, which are (5, 7). Here, x2 = 5 and y2 = 7.
Step 3: Write down the distance formula: d = √[(x2 - x1)² + (y2 - y1)²].
Step 4: Substitute the values into the formula: d = √[(5 - 2)² + (7 - 3)²].
Step 5: Calculate (5 - 2) and (7 - 3): (5 - 2) = 3 and (7 - 3) = 4.
Step 6: Now substitute these results back into the formula: d = √[3² + 4²].
Step 7: Calculate 3² and 4²: 3² = 9 and 4² = 16.
Step 8: Add the results: 9 + 16 = 25.
Step 9: Take the square root of 25: √25 = 5.
Step 10: The distance between points A and B is 5 units.

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.