Find the distance between the points (3, 3) and (3, 7).

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Question: Find the distance between the points (3, 3) and (3, 7).

Options:

Correct Answer: 4

Solution:

Using the distance formula: d = √[(3 - 3)² + (7 - 3)²] = √[0 + 16] = √16 = 4.

Find the distance between the points (3, 3) and (3, 7).

Find the distance between the points (3, 3) and (3, 7).

Step 1: Identify the coordinates of the two points. The first point is (3, 3) and the second point is (3, 7).
Step 2: Write down the distance formula: d = √[(x2 - x1)² + (y2 - y1)²].
Step 3: Assign the coordinates to the formula. Here, x1 = 3, y1 = 3, x2 = 3, and y2 = 7.
Step 4: Substitute the values into the formula: d = √[(3 - 3)² + (7 - 3)²].
Step 5: Calculate (3 - 3) which equals 0, and (7 - 3) which equals 4.
Step 6: Now substitute these results back into the formula: d = √[0² + 4²].
Step 7: Calculate 0² which is 0, and 4² which is 16.
Step 8: Now the formula looks like this: d = √[0 + 16].
Step 9: Simplify it to d = √16.
Step 10: Finally, calculate the square root of 16, which is 4. So, the distance 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 difference in their y-coordinates.