If point D is at (6, 8) and point E is at (2, 4), what is the length of DE?

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Question: If point D is at (6, 8) and point E is at (2, 4), what is the length of DE?

Options:

Correct Answer: 5.66

Solution:

Using the distance formula: d = √((6 - 2)² + (8 - 4)²) = √(16 + 16) = √32 = 5.66.

If point D is at (6, 8) and point E is at (2, 4), what is the length of DE?

If point D is at (6, 8) and point E is at (2, 4), what is the length of DE?

Step 1: Identify the coordinates of point D, which are (6, 8).
Step 2: Identify the coordinates of point E, which are (2, 4).
Step 3: Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).
Step 4: Substitute the coordinates into the formula: d = √((6 - 2)² + (8 - 4)²).
Step 5: Calculate (6 - 2) which equals 4, and (8 - 4) which equals 4.
Step 6: Square the results: (4)² = 16 and (4)² = 16.
Step 7: Add the squared results together: 16 + 16 = 32.
Step 8: Take the square root of 32: √32.
Step 9: Simplify √32 to get approximately 5.66.

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