If point D is at (5, 5) and point E is at (1, 1), what is the distance DE?

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Question: If point D is at (5, 5) and point E is at (1, 1), what is the distance DE?

Options:

Correct Answer: 5

Solution:

Using the distance formula: d = √((5 - 1)² + (5 - 1)²) = √(16 + 16) = √32 = 4√2 ≈ 5.66.

If point D is at (5, 5) and point E is at (1, 1), what is the distance DE?

If point D is at (5, 5) and point E is at (1, 1), what is the distance DE?

Step 1: Identify the coordinates of point D, which are (5, 5).
Step 2: Identify the coordinates of point E, which are (1, 1).
Step 3: Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).
Step 4: Substitute the coordinates into the formula: d = √((5 - 1)² + (5 - 1)²).
Step 5: Calculate (5 - 1) which equals 4, so now we have d = √(4² + 4²).
Step 6: Calculate 4², which is 16, so now we have d = √(16 + 16).
Step 7: Add 16 + 16 to get 32, so now we have d = √32.
Step 8: Simplify √32 to 4√2.
Step 9: If needed, approximate 4√2 to about 5.66.

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