Determine the distance between the points (2, 3) and (5, 7). (2020)

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Question: Determine the distance between the points (2, 3) and (5, 7). (2020)

Options:

Correct Answer: 5

Exam Year: 2020

Solution:

Using the distance formula, d = √((5 - 2)² + (7 - 3)²) = √(9 + 16) = √25 = 5.

Determine the distance between the points (2, 3) and (5, 7). (2020)

Determine the distance between the points (2, 3) and (5, 7). (2020)

Step 1: Identify the coordinates of the two points. The first point is (2, 3) and the second point is (5, 7).
Step 2: Use the distance formula, which is d = √((x2 - x1)² + (y2 - y1)²). Here, (x1, y1) = (2, 3) and (x2, y2) = (5, 7).
Step 3: Calculate (x2 - x1). This is 5 - 2 = 3.
Step 4: Calculate (y2 - y1). This is 7 - 3 = 4.
Step 5: Square the results from Step 3 and Step 4. So, (3)² = 9 and (4)² = 16.
Step 6: Add the squared results together. This is 9 + 16 = 25.
Step 7: Take the square root of the sum from Step 6. √25 = 5.
Step 8: The distance between the points (2, 3) and (5, 7) is 5.

Distance Formula – The distance between two points in a Cartesian plane is calculated using the formula d = √((x2 - x1)² + (y2 - y1)²).