What is the distance between the points P(3, 4) and Q(7, 1) in the coordinate pl

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Question: What is the distance between the points P(3, 4) and Q(7, 1) in the coordinate plane?

Options:

Correct Answer: 6

Solution:

Using the distance formula d = √((x2 - x1)² + (y2 - y1)²), we find d = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.

What is the distance between the points P(3, 4) and Q(7, 1) in the coordinate plane?

What is the distance between the points P(3, 4) and Q(7, 1) in the coordinate plane?

Step 1: Identify the coordinates of the points P and Q. P is (3, 4) and Q is (7, 1).
Step 2: Label the coordinates. Let (x1, y1) = (3, 4) for point P and (x2, y2) = (7, 1) for point Q.
Step 3: Write down the distance formula: d = √((x2 - x1)² + (y2 - y1)²).
Step 4: Substitute the values into the formula. Replace x1, y1, x2, and y2 with their respective values: d = √((7 - 3)² + (1 - 4)²).
Step 5: Calculate (7 - 3) which equals 4, and (1 - 4) which equals -3.
Step 6: Square the results: (4)² = 16 and (-3)² = 9.
Step 7: Add the squared results together: 16 + 9 = 25.
Step 8: Take the square root of the sum: √25 = 5.
Step 9: Conclude that the distance between points P and Q is 5.

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